Small Boat Navigation II: Dead Reckoning

Bay or coastal cruising should be like walking around your house in the dark, you should know where everything is and where not to step. After gaining a little experience, you will use your piloting skills to plan your voyages so that you maximize the navigational potential of the waters you are sailing. For example, you will learn how to lay out your courses and waypoints so that if an unexpected problem occurs (like an Aid to Navigation (ATON) has been blown away by a storm), you will have alternatives ready and mapped out. Don’t paint yourself into navigational corners and always have a Plan B.. Once this all becomes second nature, (and piloting will teach you this), you can really enjoy the convenience and reliability of a GPS because you will know that if it does fail, you don't really need it. But what happens when you can see no landmarks, when distance from land, or darkness, or bad weather leave you sailing alone, isolated from the rest of the world? The answer is dead reckoning.

The term “dead reckoning” is of uncertain origin, but probably derives from “ded” or “deduced” reckoning. It is the art and science of navigating by making judgements of a ship’s position based on its estimated speed and course and informed guesswork about the forces, like winds and currents, acting on the craft. It is used to come up with estimates of position so that the crew can anticipate hazards, or new landmarks which can be used to establish a new position or fix. In conjunction with piloting, it is the primary non-electronic means of small craft navigation, and until quite recently, it also played a major role in the navigation of large vessels on the high seas. In practice, piloting and dead reckoning are intertwined and inseparable, and both are learned and applied simultaneously by professional navigators. The traditional methods used for determining a fix, either by piloting or by sextant observations of celestial bodies, provide the raw data and initial estimates upon which dead reckoning operates. Fixes provided by GPS can also be used as a basis for dead reckoning, and the old and the new can be used as a check on each other.

For example, consider the classic case of a coastal cruiser, traveling from one harbor to another. The navigator would lay out a compass course line from his starting point to his destination and having a rough idea of the speed of his vessel, would mark that line on the chart with ticks indicating where he expected to be at certain times during the voyage. As the ship travels, these location estimates, or estimated positions (EPs), would suggest which landmarks, such as lighthouses, geographical features, or large buildings marked on the chart, would be visible and available for triangulation and determining precise fixes. As these fixes are plotted on the chart, the navigator gets an idea if his vessel is being slowed down or speeded up by currents, or if it is being set to one side of the course line or the other. A new course line, a dead reckoning or DR track, is layed out every time a good fix is achieved and plotted on the chart. In this way, the navigator always has an up-to-date estimate of his location based on solid data. If at any time his source of external navigational information is cut off, say if his ship is too far offshore to see charted landmarks, or bad weather sets in, he has a recent fix and a DR track which will give him some idea of his position for some time into the near future. The time spent dead reckoning may be a few minutes, as when a small boat is crossing a foggy harbor, or several weeks, as when a ship is crossing an ocean, but the principle is always the same. The dead reckoning position will be all the navigator has until he gets the next fix, so it is essential that fixes be taken frequently when conditions are good so that when they deteriorate a solid, recent position will be available to base estimates. Many navigational techniques, such as piloting via triangulation, radar ranging, LORAN, radio direction finding, and even celestial, all require a rough idea of one’s location as a seed position, so this is essential. Even a ship successfully navigating with GPS should maintain a good DR track as a check and backup in case the GPS should fail or be misinterpreted.

After each fix is plotted on the chart, a pencil course DR track is drawn to the next waypoint (destination or turning point) and ticks on the course line drawn with the time the ship expects to get there. These estimated positions are drawn with circles around them (proper fixes are marked with triangles), also with the time. Using the familiar “DRT” equation, Distance equals Rate times Time, or D = RxT and the laws of algebra, we can also solve this expression for either Time (T = D/R) or Rate (R = D/T). There are nautical slide rules that can do this calculation for you, or you can use a pocket calculator. The point is if you know any two of the variables in the DRT equation, it is easy to solve for the third. For example, if you have been traveling for 20 minutes since your last fix at a speed of 12 knots, you will be 4 nautical miles along the DR track. D = RT where 4 = 12 x 1/3. (Remember, 20 minutes is a third of an hour.)

A knot is the nautical term meaning “1 nautical mile per hour”. Never say “knots per hour”. It is lubberly and not to be countenanced. A nautical mile is roughly 2000 yards, or 6076 feet. Nautical miles are convenient at sea because the nautical mile is equal to 1/60 degree, or one minute of latitude, and the latitude ticks are always drawn on the east and west sides of the chart. Use the dividers drafting tool to measure off distances from the latitude scale and transfer them to your DR track, or conversely, to measure distances on the chart and scale off the distances using the latitude scale. Nautical charts usually employ the Mercator map projection, so distances on the chart can be measured directly off the latitude scale with your dividers. You don’t have to learn all this today, dead reckoning is something you’ll need instruction and study for and plenty of practice. Just keep in mind that the DR track on the chart will serve as a record of your voyage and a paper computer to help solve navigational problems. Your sources of information will include your compasses and your log (the device which indicates your speed through the water). Incidentally, it is important to keep in mind that the log measures speed through the water, you need to know speed over the ground, so a constant comparison with your speed as revealed by your navigation and that indicated by your log will give you an insight into the currents affecting your boat.

The practice of navigating a boat using piloting and dead reckoning all revolves about the DR plot drawn on the chart. Here is the record of all navigational observations and calculations, a projection of future plans, and all the information the makers of the chart were able to include, all drawn in a systematic manner any seaman will be able to understand at a glance. Make sure that if the vessel has to maneuver, or deviate from its course, that the DR track is updated to include this change of course and/or speed. The DR track represents the best possible estimate of your position until you plot your next fix. It must reflect every maneuver and the exact time when it occurred.

Dead reckoning also allows the skipper to develop estimated positions based on partial navigational information, in addition to calculations or extrapolations of course and speed. For example, suppose only one feature on shore is available for a bearing. The vessel will lie somewhere on that line of position (LOP), but exactly where will not be known for sure. The navigator can use as an estimated position (or EP) the intersection of the LOP and the DR track. This is not as trustworthy a position as a proper fix, but it is better than most estimates because some real observational information contributes to the estimate. Later on, after that landmark is no longer visible, a new landmark may come into view. The pilot can then shoot a bearing on that, plot the LOP, and use his knowledge of his course and speed to “slide” the previous LOP along the DR track using his parallel rulers. The course and speed are already roughly known, so the old LOP is moved along that DR course (keeping the same angle to the chart grid) for a distance corresponding to the time since the last bearing (using the D = RxT equation). The new and old LOPs, along with the DR track, will provide a triangle on the chart and the boat will probably be somewhere near it. Of course, this is not as good as a proper fix made up of two or more simultaneous LOPs, but it’s better than a sheer guess. This procedure is called a running fix, and very often it is all a navigator has available when sailing down a barren coast where charted features are few and far between.

There are all sorts of tricks you can employ to come up with a serviceable EP, or to help stay on track. For example, suppose there is a featureless island near your boat, no landmarks are visible on it but you can always shoot bearings to either end; the tips of the island, after all, are landmarks, they are plotted on the chart! Of course, you will have to convince yourself you are actually shooting the ends of the island, not a cape or promontory which obscures your view of the extremities of the land. These are called tangent bearings. Another trick is to select your course so that if you have to make a turn to a new course as you approach your destination (perhaps to avoid a reef), the point where you make your turn will be one where some landmark bears a certain bearing. As you approach the spot where you plan to make your turn, you shoot bearings until the turn bearing you calculated earlier turns up on your compass. A related technique is the danger bearing, where you calculate ahead of time some bearing which must be greater or less than some value to ensure you are in safe waters. Another technique is the range. For example, if you know a light on shore can be seen from, say, 21 miles away, draw an arc of radius 21 miles on your chart, centered at the light and when the light comes into view you know you are somewhere on that arc. Range arcs are LOPs too, and they can be crossed with others to give a position. Again, none of these techniques is as reliable as a proper triangulated fix, but they are far superior to nothing at all. On the other hand, a range derived with your boat’s radar can be extremely accurate. Piloting and dead reckoning can be done with radar too, it is not just a collision avoidance system, it is a very useful tool for the navigator although it sometimes is difficult to properly interpret radar images.

It can’t be emphasized too much that coastal piloting and dead reckoning are not skills that can be picked up by reading a magazine article or two. The actual mechanics of plotting fixes and taking bearings as well as laying out and maintaining a DR track are fairly straightforward, but integrating all this information into a navigational plan requires experience. Let’s look at a typical navigational problem.

Your task is to sail to an island offshore, well out of sight of land to the east. The island is long and thin, and it lies across your path. The harbor which is your destination is at the southern end, the rest of its coastline is bordered by dangerous reefs. There are no aids to navigation on the island, or on your way there, available to guide you. If you should miss the island in the dark, you could sail on past it out to sea. The usual drill is to simply draw a line on the chart from your point of departure to your destination, determining the course and distance from the chart, and getting underway. Your knowledge of your boat’s speed, or your log, will give you a rough idea of your speed, and how long it will take you to get to your destination, so you will mark off your DR track where you expect to be at certain convenient time intervals (an hour, a day, whatever the length of the trip requires). You try to plan your voyage so you will arrive at the vicinity of the island well after daybreak, not too early or you might stumble onto it in the dark, not too late because you want a full day’s daylight to work with once you start getting near it’s dangerous waters.

It’s highly unlikely your vessel will remain on its DR track throughout the entire voyage, or that you will adhere to your schedule as planned. Wind and current will constantly throw you off, so it is possible you will be quite off your original DR track by the time you get to the vicinity of the island. If you are set to the north of your DR track, you will hit the island for sure, but recall the harbor is at the southern end of the island, if the current sets you to the south, you might miss the island altogether in the dark or in bad weather. It is better to set your original course and speed to the center of the island, so if you’re off a bit you are not as likely to miss it.

As you sail away from your home port, take as many fixes as possible on known landmarks and determine how your true course and speed match up to your DR. This will give you some idea of how the set and drift induced by wind and current affect your boat. Make sure any maneuvers you make are reflected in your DR plot. Once you’re out of sight of land, you’re going to have to use this knowledge to help correct your course. As you approach the island, take tangent bearings to try and develop a fix, and if any landmarks on the island are marked on the chart, try and locate them to verify your position. Any information on the chart might help develop an estimated position. For example, if the island is surrounded by a shallow shelf that is marked on the chart, keep an eye on your depth finder. Suddenly crossing into shoal water is a rough, but useful LOP! It might tell you how far offshore you are where distances might otherwise be difficult to judge. If you also have a GPS aboard, navigating with it while you practice these traditional skills is a great way to learn.

Even if your GPS and other electronic equipment are functioning perfectly, the ancient arts of piloting and dead reckoning are a useful backup for emergencies that also will enhance your enjoyment on the water, as well as give you great confidence and peace of mind. But most important, they will put you in spiritual connection with all the generations of mariners that went to sea before you. It’s the difference between being a weekend boater and being a seaman.