Dead reckoning (DR) navigation was the way early mariners deduced their speed. In the days before the invention of celestial navigation DR was an essential tool for plotting a ship's global position when out of site of land. Christopher Columbus used this method on his early voyages, although celestial navigation was, by then, coming into its own.

The use of the compass for navigation began in Europe in the late 12th Century, but the only way to work out the distance travelled was by knowing the speed of the ship. Only then could a map be charted with any degree of accuracy.

Distance travelled is the product of speed and time. Time was measured with an hour glass before the invention of an accurate chronometer, and every hour a piece of flotsam, usually a log tied to a length of rope knotted at regular intervals, was thrown overboard. The speed of travel was calculated from number of knots which were pulled into the sea in the specific time marked by the hour glass (To this day, nautical miles per hour are still measured in knots). Once the distance was calculated and the compass bearings noted, the progress of the ship could be plotted on the chart.

In emergency situations, such as when there is a failure of electronic navigation equipment, DR is still used today. This method, if performed carefully, can achieve around 90% accuracy.

You may ask why we continue to use dead reckoning (DR) and paper charts in an age of electronic positioning systems (such as LORAN, GPS, INS and dGPS which combines INS and GPS to produce a three dimesional plot, even when GPS reception is not possible, and ECDIS-N, which takes LORAN, GPS and INS plots and places them on a digital chart). The first step to understanding DR navigation is to understand the historical necessity of DR sailing. An excellent writeup on this history exists, as written by Blue Dragon. The key difference between historical and modern DR must be emphasized: modern DR is graphical rather than mathematical, and is used as an aid to a total navigational picture rather than the principal means of navigation. However, the DR plot remains essential for three reasons:

First, it standardizes plotting procedures so that anyone familiar with navigation can pick up your chart and plot and immediately have a mental picture of the navigation situation (what and where are the next hazards, what evolutions will need to occur in the near future, what options are available in case of an emergency, etc.) Second, DR ensures the position of the ship is constantly updated, as actual fix intervals may be separated by a large period of time (especially for offshore cruising or racing). It also ensures that the position of the ship is known even into the future, providing the skipper, afterguard, or captain with a higher level of situational awareness. Finally, it supersedes electronic navigation as no ship relying solely on one aid to navigation has ever been found innocent in a court of admiralty. DR establishes a historical record for legal purposes, and shows seaman-like actions taken in advance of the collision, should one occur.

To perform DR navigation, begin as soon as you establish a fix on the chart. Label this fix with a circle (1/4") around the fix if it was achieved by visual bearings, an equilateral triangle with 1/4" sides if it was achieved by one or more electronic sources (radar soundings, fathometer soundings or GPS coordinates, for example) or a combination of electronic and visual means. Use a square with 1/4" sides if the position was established by inspection or estimation (for example, you are tied to the southern point on a pier shown on the chart, or if you estimate a position based on the current). Label the fix with the four-digit 24-hour time. Then, immediately draw a ray from the fix on your course. Label this line with your course and speed by writing "C(COURSE)" above and "S(SPEED)" where (COURSE) is your three digit heading, and (SPEED) is your speed in knots. We are now ready to start taking DR positions. A DR position is labeled by a small semi-circle, about the same size as your visual label. It is labelled by only the last two digits of the time, unless the time is the top of the hour, in which case you write all four digits. Follow the six rules of DR to know when and how to draw DR points:

The Six Rules of DR

  1. Every hour, on the hour.
  2. At the time of every course change. Label the new course line, drawn from the DR point, with "C(COURSE)"
  3. When motoring, at the time of every speed change. Label the old course line at the DR point with "S(SPEED)"
  4. At the time of obtaining a single line of position by either visual means, a visual range where two objects align, or by electronic bearings such as RACON beacons.
  5. At the time of obtaining any fix or running fix.
  6. The instructions for drawing course lines and DR points: a new course line is drawn at any fix or running fix, but never for an estimated position or a single LOP. When drawing DR points, always draw two DR points for the next two fix intervals ahead of the last fix or running fix.

The following is an example of how to draw a visual fix at 0952, with an easterly course, at a speed of 11.4 knots.

                  58      1000       04
 0952 C090        ∩        ∩           ∩     

Note that the semicircles should touch the course line and there should be a dot in the middle of the O, something I can't simulate with ASCII.

Got it? It looks like a lot to memorize, but once you do this for a living for a while it comes naturally. The fastest way to make it natural is to force yourself to do it every time you set sail.

Now that you've mastered when to place a DR, you need to know where to place the DR. This is where we must be able to calculate speed, distance and time. Simply use the calculation that distance {nautical miles} = (speed {knots})(time {hours}). This equation will always work, however sometimes it is inconvenient. That is where the sixty minute rule, six minute rule and three minute rule come into effect. Let's assume that a nautical mile is 2000 yards- it's pretty close: the error created by assuming a 1:2000 ratio is much smaller than the error created by the width of your pencil lead on most charts.

  1. Three Minute Rule: The distance in yards travelled in three minutes is equal to speed in knots multiplied by 100.
  2. Six Minute Rule: The distance in nautical miles travelled in six minutes is equal to speed in knots divided by 10.
  3. Sixty Minute Rule: The distance in nautical miles travelled in sixty minutes is equal to the speed in knots.

As you can see, with these three rules we can make many distance calculations in our heads quite easily. For example, fifteen minutes is five three minute rules: speed in knots times 100 times 5. Once we have a distance, we simply place a DR mark on the course line that distance from the last fix.

For more information on how Dead Reckoning is used in professional navigation, consider reading about currrent sailing, precise nautical piloting and celestial navigation.

I have to quibble with a few points on this one, though it's mainly a question of doctrination.

The way the (British) Royal Navy do it, you fix at different intervals given where you are.

In Pilotage waters - every 3 minutes

In Coastal Passages - Every 6 minutes

In Ocean Passages - Every 12 minutes (Loran/GPS)

You would then DR on from every fix, using the 6 minute rule. To avoid any of the multiplication inherent in the rules above, the RN version is simple - the number of Cables (1/10ths of a Nautical mile) travelled in 6 minutes is equal to the speed in knots you are doing - for example, at 12 knots, 2 cables per minute. This makes things very easy if you have a stopwatch - you know every 30 seconds that tick by on the stopwatch, you have gone another cable down your nav track.

Anyway, I'm getting sidetracked. Every fix, you put a DR on, be it 3 minutes or 6 depending on how frequent you are fixing. This will give you a rough estimate of where you will be, not taking into account the effects of wind or tide. The DR is marked with a vertical dash on the line and 2 figure time. However, for accurate reckoning of your position at a given time, you use what is called an EP - Estimated Position. You have 2 fixes on while steering the same course, you simply draw a line through the two fixes and continue it in the direction you are travelling. You then take the dividers and measure the distance between the two fixes, which has been travelled in a known time period - say for our purposes, 6 minutes. You use the chart to find out that distance, and you know your speed in knots. You use the distance between the fixes when marking off on the line where you will be in the next 6, 12, 18 minutes etc. However, instead of a line through your track line, you use a triangle, with the same 2 figure time. Thus you have an EP.

US Army Training - Individual Land Navigation

Dead reckoning is one of the techniques used by soldiers for navigating cross-country on foot. Personally, I try to refrain from using dead reckoning, as it tends to be inaccurate on foot, due to shifting terrain. A soldier, or any person trekking/hiking, will unknowingly flow with terrain due to fatigue, weight of equipment, and other factors like illumination. The concept and execution of dead reckoning is simple, however I suggest only using it at night when illumination is minimal, or if you are in an unknown location headed towards a possible checkpoint (an identifiable terrain feature). With dead reckoning, the navigator has a known starting point and azimuth he/she is traveling on, and hopefully a known distance.

Using a lensatic compass and map, plot your starting point and end point. Determine your azimuth and record it in your navigation log or something similar. Stand at your start point, shoot your azimuth using the most accurate means. Pick an object in your path about 100m along your azimuth and move to it. If you know your pace count, be sure to keep it. If not, the average male with a heavy load will use 62. That is, every time your left or right foot hits the ground, count 1. Every 62 should be 100m. To accurately determine your pace count, count every other step along a 400m route and divide by 4.

Simple: Point, shoot azimuth, walk, rinse and repeat. Continue and be sure to check your azimuth often.

Also, when determining your azimuth, be sure to check the declination diagram on your map. It indicates the difference between grid north (north on your map), and magnetic north (north on your compass). This will change depending on your location in the world. All you have to do is add the declination angle to your grid azimuth and that is your magnetic azimuth.

Personal Experience
When I am navigating, I write my azimuth and distance on my hand so when I check my azimuth I can glance at my hand in case I forget. Fatigue is a bitch.

Dead reckoning is only useful if you cannot associate the terrain around you with your map. Dead reckoning is a painstakingly slow way of navigating and should only be used in conjunction with terrain association, and pace count for less experienced navigators.

One more point: Trust your compass. During long range movements you are going to be fatigued, wet, and in pain. Your mind is going to start playing tricks on you. You will be crossing a particular terrain feature, and your going to think, "Hey, I think I should be going this way." but your compass will say otherwise. Trust your compass! It isn't going to lie to you unless you are doing something stupid or have a defective compass.

Note: This use of the term Dead Reckoning is used in the United States Army. The definition may differ depending on usage.

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