Accurate DR without plotting

I enjoyed reading two recent articles on celestial navigation ("Recollections of a longtime celestial navigator," and "A celestial tune-up in time for landfall," Issue No. 64).

Not long ago I went to my eye doctor for an annual checkup. He is an Air Force Reserve major and a navigator. We always manage to get in a few words about celestial navigation during my visits. As he began to check me, he told me he had just returned from a flight in a hurricane hunter, and "guess what they had aboard?" he asked. "A sextant." It seems that despite all the sophisticated electronic nav gear these planes are equipped with, they still carry the old hambone. Of course, if possible, they feed their information from a sight into the computer and get a solution, but if the computer is down, they use a set of tables just like us earthlings.

Mr. Stephens speaks of standard forms. I don’t like them either, and I refuse to let my students use them. In 1959 I was aboard the U.S.S. Beatty, which was operating out of Key West chasing tame submarines and training reserves. As a reservist myself, I had the detail to drill younger reserve officers in celestial navigation. One day, they had their sight reduction forms laid out on the chart table when someone opened the weather door to the wheelhouse. The lee door was already open and the essential forms all went over the side!

Mr. Stephens also writes of shooting sights at night. It does, indeed, work. During WWII, I was the executive officer in a 110-foot sub-chaser. On one occasion we were sent out to rendezvous with a Chilean merchantman several hundred miles south and west of Oahu. All we had to navigate by was the old reliable hambone and hack. But the sights were few and far between until the evening for rendezvous; we needed a fix. Well after evening twilight the sky cleared. When the full moon got high in the heavens, I took a round of stars and got a good fix. Although I had shot stars on reciprocal bearings hoping to reduce some of the error caused by a poor horizon, I found I didn’t need reciprocal bearings; I got a very good fix. I have also shot stars on the dark of the moon long after evening nautical twilight and have gotten good results.

The electronics aficionados always ask, "What do you do when the sun is not out?" I answer the sun will come out again someday; that GPS or other gizmo won’t be fixed until you make port. And the skies do not need to get too clear. Any competent navigator should be able to get a sight by wing shooting the sun as it jumps across a rift in the clouds; with just a little more practice and planning the same thing can be done with stars.

What do you do if there is no horizon? LCDR. W.M. Riley, USCG, since retired, reviewed the syllabus I organized for Delagado College several years ago. He sent me a little squib on a system he claims he has used. When the horizon is obscured by fog or some other reason, LCDR. Riley uses Table 22 of Bowditch, Dip of the Sea Short of the Horizon. This may not be what Table 22 was intended for, but it could be better than not getting any sights.

All this is good, but I wonder how many cruising yachts carry Bowditch. Going to sea without Bowditch is like going to Sunday school without your bible. All you need to navigate anywhere in the world is Bowditch, a Nautical Almanac, and a chart. If you do not have a chart, a good set of sailing directions is better than nothing. I took the yacht El Toro across the Gulf of Fonseca, on a voyage from Corinto, Nicaragua, to La Union, El Salvador, without a chart; I did have a set of sailing directions. Navigating this way can be fun, too, and useful. And it fits right in with the method of so many old-timers: "latitude, leadline, and Lecky." I recall on one trip to West Africa, my engineer, a very intelligent man from the Cameroon, began to get just enough knowledge of navigation from watching me to think he had learned all he needed to know. I simply quit plotting and did my dead reckoning by Table 3, Bowditch, in my notebook. It almost drove poor Joseph (in West Africa one pronounces that "Joe Seph," as if it were two words) bananas!

If you take the explanation of the tables in Bowditch and run the formulae through a calculator, it may surprise you how many of these solutions can be worked easily and quickly on a calculator. Take an example from Table 3: A vessel takes her departure from a position at Latitude 31° 47′ 22" N, Longitude 61° 47′ 28" W, and sails on a course of 068° T for 197 miles. What is your DR position?

Open Bowditch to Table 3, course 068° T, distance 197 miles, and get: Difference of latitude of 73.8 miles, and a departure of 182.7 miles. The difference in latitude of 73.8° is 1° 13.8′. Add this to your latitude of departure, which we call latitude left, because this is the case in navigation where the term departure is used with two entirely different meanings. The first meaning is the point from which a vessel departed or left. The second meaning of departure is the difference in longitude expressed in nautical miles. As 068° is N 68° E, you are making northing. Add the difference of latitude to the latitude left:

Lat left

31° 47′ 22" N

DR Lat

33° 01′ 10" N

The departure 182.7′ must be converted to difference of longitude. But a minute of longitude equals a nautical mile only on the equator; at the poles a minute of longitude equals zero. So to convert departure to difference of longitude, you must first find the middle latitude by adding the latitude left to the new DR latitude, and dividing the sum by two. This gives a middle latitude of 32° 24′ 16". Now enter Table 3 with 32° as a course. Find the departure nearest to 182.7, which is 182.3 in the difference of latitude column, and opposite in the distance column is the difference of longitude. The difference of longitude as found in the distance column is 215. Your difference of longitude is 3° 34′ 59". As 068° also has an easterly component, you are making easting. Subtract this difference of longitude from the longitude left, which is your longitude of departure.

Long left

61° 47′ 28" W

DR Long

58° 12′ 29" W

You could have interpolated for the differences between tabulated departures, and the middle latitude not being exactly 32°, but it likely would not have been worth the bother. Another way to convert departure to difference is to use Table 6 of Bowditch. From Table 6 you find the length of a degree of longitude at 33° is 50.461 miles, and at 32° a degree of longitude is 51.022 miles. Without interpolating, take 182.7 and divide it by 51.022. The difference in longitude here is 3° 34′ 51", which is 27" difference between the two methods.

With Table 3 you can work up a DR much quicker than by plotting. And with a calculator, you can do it much quicker than with Table 3.

Try this sometime. I’ll bet you will get a kick out of your fellow navigators’ reactions when they see you keeping your reckoning, as we used to say, without a plotting sheet in sight.

And now a disclaimer: I have been accused of not believing in electronics. Not true! I carry two loran receivers on my boat Zubenelgenubi. If I make an ocean crossing, I hope to have a GPS aboard. But, I would not hesitate to sail to England without a loran or GPS. I would not go if I had all the electronics in the world but was without my sextant.

Warren Norville is a retired Naval Reserve officer and a navigation instructor who lives in Mobile, Ala.

By Ocean Navigator