Editor’s note: We’re revisiting this series on navigating by the sun, moon, planets and stars in the age of GPS because celestial nav is not only a viable backup to satellite navigation, but it is also a skill that ocean voyagers should have in their toolkit. In this series, we’ll cover all the basic knowledge you’ll require to get up to speed on this elegant and rewarding technique for finding your way at sea. Click to read Part 1, Part 2, Part 3, Part 4, Part 5, Part 6 and Part 7.
In this installment, we’ll cover running fixes and the hierarchy of positions from dead reckoning position to multiple simultaneous lines of position fixes.
In the previous installment of the series, we looked at how the HO 249 sight reduction tables work and how to plot a line of position (LOP). This is the bedrock skill for all of celestial navigation. Everything in this method of position finding rests on being able to calculate and plot an LOP. (In this installment of our series, we also include the information for a basic sun sight reduction so you can practice what you’ve learned so far.)
From the single LOP of the sun, we can build our skills until we get to the multi-body fix involving multiple LOPs of objects all taken at the same time — for example, a round of star sights or multiple sights of stars, plus planets or the moon.
There is a hierarchy of position types that go from good to better to best. We’ll discuss this hierarchy at the end of this installment.
Before that, however, let’s look at the next step after learning how to do a single LOP from a single sun sight. This next step is something called the running fix of the sun.
Fig. 1 shows the situation after an 0800 sun sight. The 0800 DR position is the result of speed and course information recorded and plotted since the last fix. The EP is the box on the LOP. This is the best guess of where we are based on integrating the DR and LOP information. Fig. 2 shows the same scene three hours later at 1100. The DR track has been run forward from the 0800 EP, and another sun sight was taken at 1100 and plotted as an LOP. To create the 1100 running fix, the 0800 LOP is advanced along the DR track to the 1100 DR position. This is another advantage of creating the 0800 EP: It starts the DR track from the 0800 LOP so that the 1100 DR position is an advanced point of that LOP. The advanced LOP is labeled with “0800–1100,” indicating that it has been advanced. The running fix is the intersection of the advanced 0800 LOP and the 1100 LOP.
The running fix
One difficulty with relying solely on sun sights is that it is not possible to get two LOPs from the sun to cross if they are taken at the same time. To get around that, a special type of fix can be used: the running fix. A running fix is the position formed by crossing two LOPs taken at different times. The first LOP is then advanced along the DR track to the time of the second LOP.
A running fix is not as reliable as a true fix because it relies on the accuracy of the DR information collected during the time between the two LOPs. Nonetheless, it is valuable for navigating both out in the ocean and coastally because the first LOP (the one that is advanced along the DR track) gives the navigator additional information that helps to refine the most current LOP. An accompanying example is given here with plotting information from 0800 and then again at 1100. At 0800, the navigator took a sun sight and plotted the LOP as shown above in Figure 1.
Now the navigator is faced with two pieces of information: the DR position and the LOP. When navigating on a yacht (with its less precise DR capabilities), it makes sense to combine both these pieces of information.
The best way to do this is to create an estimated position (EP) on the LOP. This EP merges the information on the LOP with that of the DR (more on the relative value of various types of positions is given below in the hierarchy of values section). To create an EP, find the point on the LOP closest to the DR position. This is done by dropping a perpendicular line from the LOP to the DR position. Where the perpendicular crosses the LOP is the spot that we will mark as our EP.
The EP is the best guess of where the boat is on the LOP because that is the position on the LOP closest to where the navigator thought he was (the DR position). The DR track should be continued from the EP and not from the 0800 DR position. This makes sense because even if we have been fastidious about getting our DR info, we just took a sight and plotted the resulting LOP, and that is higher on the hierarchy of positions than a DR position.
This situation is plotted in Figure 1. From the 0800 EP, the boat sailed on a course of 170° for three hours at a speed of 6 knots until 1100. At 1100, the DR track has been advanced from the EP at 0800. In Figure 2, an additional sun sight has been taken and plotted. Now there are two LOPs taken three hours apart. The 0800 LOP needs to be advanced along the DR track. Because we started the DR track on the LOP at the 0800 EP, the LOP may be advanced to the 1100 DR position. This is because when we have an LOP, by definition it means that we are somewhere on that LOP. We could move each point on the LOP individually in the same direction and distance to the 1100 DR position; however, it’s more efficient to just move the entire 0800 LOP at once down the DR track to the 1100 DR position.
To do this easily, just line up your parallel rules with the 0800 LOP and then move them down the DR track so that a parallel line can be drawn through the 1100 DR position. This is an important point. You advance the earlier LOP along the DR track to the DR position of the time you took your second LOP. The times of the LOP and the DR position must agree.
In our example, this new LOP should be labeled: “0800–1100.” This immediately indicates that the LOP has been advanced from 0800 to 1100.
The running fix occurs where this advanced LOP crosses the 1100 LOP, which is the most up-to-date LOP. This position should be labeled: “1100 RFIX.” We start a new DR track from this RFIX.
This diagram shows multiple LOPs derived from sights on different celestial bodies taken at the same time. When these LOPs are plotted we get a fix position where the LOPs cross.
The hierarchy of positions
Now let’s discuss the hierarchy of positions. They’re like the various hands in poker; some have more value than others. This hierarchy reflects the advantage of refining a position with additional information.
DR: The basic position is the DR position that is based on the course and distance traveled since the last fix. Some navigators integrate additional information into their DR position, like leeway and estimated current. Others keep it “pure.” One reason to stay with the pure DR is that it can then be compared with a fix to determine the set and drift of the current. The DR position is really the bedrock of all navigation. It will enable a navigator to not only determine the set and drift of current, but also create more accurate running fixes.
EP: Next on the scale is the estimated position (EP). This is broadly defined as the combination of a DR position with other positional information. This could include current information, leeway or an LOP. The common way to combine a DR position with an LOP is to drop a perpendicular from the LOP to the DR position. The EP is the point on the LOP that the perpendicular intersects.
RFIX: One step up from an EP is a running fix. As described above, the running fix uses LOPs taken at different times to create a fix. The earlier LOP is advanced to the time of the second LOP by progressing it along the DR track from the first time to the DR position that agrees with the time of the LOP. This is better than an EP because it uses information from two LOPs. It is definitely a step down from a fix because the advanced LOP is subjected to any inaccuracies in the DR.
FIX: At the top of the heap is the fix. This is the intersection of two or more LOPs taken simultaneously. (The slower you’re moving, the longer the time period that “simultaneously” applies to.) With celestial navigation, fixes are most commonly taken at morning or evening twilight using stars and planets. It is also possible to use the sun and the moon when the moon is available during the day. For star fixes, three LOPs are much preferable to just two. The third LOP provides a check in case one of the sights is poor. The result will be an intersection that forms a large triangle. Without this third LOP, there is no way of determining if one of two LOPs is poor. (Actually, more LOPs are better because then the proper position will become clear with the addition of more LOPs.)
Finally, accompanying this installment is Problem 1, which is a sun sight.