A defense of the running fix
To the editor: I was intrigued by the recent article by Prof. John Karl (The nonsensical running fix, Issue #190) on running fixes in celestial navigation.
In the 1960s — long before GPS — I was a navigation officer on tramp ships. We must have made thousands of celestial observations to find our position at sea. All we had was a sextant, time piece, nautical almanac and sight reduction tables. Most of the time, multiple LOPs went through the same position; giving us an accuracy of half a mile.
The first thing I noticed in the article was the distinction made between the dead reckoning (DR) position and the estimated position (EP). Some people believe that dead reckoning was derived from deduced reckoning, whereby you use all the information at hand to arrive at a conclusion. Mr. Karl uses only part of the available information to come up with a DR position and then upgrades this by using leeway, currents, etc., to arrive at an EP. Common sense dictates to use all the available information right away.
Then Mr. Karl goes on: “Short-run fixes, such as in a round of star shots taken over a relatively short time from a slow vessel may well have better DR accuracy than LOP accuracy...”
In case of a bad horizon, I would agree. However, if your celestial navigation skills are so inept and you put more faith in the DR position than in your fix, you may want to consider hanging up your sextant.
I have trouble following the professor’s reasoning, as I am not sure what’s wrong with advancing an old LOP to a new one. When I was 3rd officer I stood the 0800 to 1200 watch and used to shoot the morning sun with an azimuth (Z) of less 150° when we were north of the sun’s declination, or more than 30° if the sun passed north of our position. In either case, the morning LOP would form an angle of at least 30° with the 90°-270° noon sight. When the sun is close to your zenith, Z changes very fast from east to west and the time between sun shot and noon sight can be short, so errors in advancement remain small.
When I was 2nd officer and stood the 1200 to 1600 watch, I used to shoot the afternoon sun when Z was about 30° different from the noon sight and advanced the latter. When I felt really ambitious and the moon and Venus were above the horizon and the LOPs made good cuts, I shot those in addition to the sun to make brownie points with the Old Man (the Captain). At dawn or dusk we shot a number of stars.
With reference to the article’s last paragraph in the second column on page 52, I still have trouble understanding how the EP or DR position can be better than the RFIX. The problem of LOPs crossing at narrow angles is very easy to solve. Don’t use them; wait for a better opportunity! When you miss the noon sight, due to let’s say clouds obscuring the sun, or fog at the horizon, but are able to take a sun shot within a few minutes before or after meridian passage, there is a simplified calculation to convert the LOP into a noon sight.
—Don Dykstra is a former merchant mariner who lives and works in Houston, Texas.
John Karl responds: Dead reckoning usually means determining a ship’s position by advancing a previous position using courses and distances. The EP is the most probable position of a craft, determined from incomplete data or data of questionable accuracy (Bowditch, 1962). In this spirit, as I described in the article, I used DR to mean a position that was degraded by using any information of lesser quality, and the EP to be the position whose accuracy was upgraded by the addition of better information, such as by the acquisition of an LOP.
In the case of a round of star shots, the dead reckoning referenced is between LOPs within this round. Because of the relatively short time between these LOPs, the DR accuracy is usually better than celestial LOP accuracy, particularly in slow moving vessels. This is an example where the traditional running fix (TRF) is, indeed, appropriate. And as the article said, we’re addressing the opposite case, where the DR accuracy is worse than the LOP accuracy.
As can be seen in the article’s Figure 3, the trouble with the TRF is that it assumes the DR track perpendicular to LOP1 is perfectly accurate, while the DR track parallel to LOP1 can have an unlimited error. This is never true, in fact, it’s nonsensical. This is equivalent to saying we had no idea whatsoever of the ship’s position along LOP1 when it was acquired — again, never true.
In contrast to the TRF, the EPRF assumes only that (1) DR2 is the best estimate of the ship’s position, given all the information used in the DR, and (2) that LOP2 is appreciably more accurate. Thus any such newly-acquired LOP must improve the DR position, even one parallel to LOP1, as shown in the nearby figure. To not use the information from these new LOPs would be nonsensical.
In the old days when longitude was determined solely by dead reckoning, noon sun shots taken on successive days determined the latitude. Then just before a noon shot, the ship’s current position was the previous day’s noon position updated by DR. This current DR position was then improved to an EP by the addition of a new east-west sun line. In plotting terms, this is drawing a line from the current DR position perpendicular to the new sun LOP — that’s an EPRF that even the old man accepted.