Dead reckoning is the method of navigation by which your position is determined by means of the direction and distance traveled from a known point of departure. A vessel underway is moving through the water, which is always changing. The vessel might leave point A, steer an exact course according to the true bearing between point A and point B, and still wind up a long distance from B, depending on how much leeway your vessel makes. Estimating the distance traveled seldom gives you a exact fix.
The dead reckoning (DR) position is only an estimated position. A fix is a exact position from the intersection of two or more lines of position. A DR position is not a fix, but is calculated from the last fix obtained. In piloting, a fix is obtained by bearings taken on objects whose locations are charted. In celestial navigation, position (fix) is determined by observations of the heavenly bodies. When a ship out of sight of land is prevented by bad weather from taking celestial observations, she must navigate by other means. Normally, electronic navigation is used when the ship is located in an area where it is available. If nothing else can be used, the ship must navigate by dead reckoning.
Plotting a DR Track
In early sailing days, "dead log" was one of the methods used to measure ship's speed. The means of measuring speed consisted merely of timing the interval between which a piece of wood tossed overboard at the bow was off the stern. The length of the ship being known, it was a simple calculation to estimate the vessels speed. The dead log is considered by some as one source of the word "dead" in dead reckoning. Another theory is that dead reckoning originally was "deduced" reckoning. Shortened in the logbooks to "ded" and "a" somehow crept in, making it "dead." Whatever the source, nothing is really dead about dead reckoning.
Following a ship's DR track from one fix to the next is a continous process while underway. A constant check on your approximate position is needed by the navigator for many reasons. In celestial observations, it lets you locate your assumed position reasonably close to the ship's actual position. How is the DR track plotted? Suppose that a fix , determined at 0900 by celestial observation, piloting, or electronic navigation, located your ship in latitude 44° 36.5' N, longitude 124° 03.5' W. It is your last fix, and your DR track begins at this position, along the line of the true course steered. Assume that your course is 220° T. You set your parallel rulers or triangles on 220° and shift them to the fix, then draw a line from the fix bearing 220° T. As long as you stay on that course, your DR track will advance along this line. Let's say you're steaming at 20 knots. In 1 hour, or at 1000, your DR position will be 20 nautical miles from the 0900 fix, along the 220° T course line. The line bearing 220° from the fix is the course line or rhumb line. Label it "C 220° " above the line, and "S 20" for a 20 knot speed below the line. Label the fix 0900 and the DR position at 1000.
The 1000 DR represents where you will be if you travel exactly 20 nautical miles on C 220°, that is, if you are not set to either side of your DR track. If you have a strong headwind or a head sea against the bow, chances are that you won't quite make 20 nautical miles. Although the helmsman may keep the vessel on exactly 220°T for every second of the hour, it is probable that a wind, current, or a combination of the two elements will work to set the vessel to one side of the course. For this reason, it's unlikely for the DR position to match with your actual position, even after steaming only 1 hour.
Lines of Position
Piloting is the use of 2 or more lines of position, the intersection marks the ship's position. A line of position is determined with reference to a landmark. For this purpose, a landmark must be identified easily, and its position must be shown on the chart that you are using. Lines of position are of three general types: ranges, bearings, and distance arcs. Two instruments used in taking bearings are the bearing circle and alidade. A bearing circle is a nonmagnetic metal ring equipped with sighting devices. It is fitted over a gyro repeater or a magnetic compass. Let's say you want to take a bearing on a lighthouse. First, put the bearing circle on the gyro repeater or magnetic compass, and make sure the vanes rotate freely. Next, line up the vanes in a way that when you look through the opening in the near vane, you see the lighthouse directly behind the vertical wire in the vane. You then read the lighthouse bearing on the prism at the base of the far vane.
A alidade is a telescope equipped with crosshair, level vial, polarizing light filter, and internal focusing. The telescope is mounted on a ring that fits on a gyro repeater or magnetic compass. The optical system simultaneously projects an image of approximately 25° of the compass card, together with a view of the level vial, onto the optical axis of the telescope. By doing this, both the object and its bearing can be viewed at the same time through the alidade eyepiece.
Ranges
A ship is on a range when two landmarks are observed in line. This range is represented on a chart by means of a straight line through two known chart symbols. The line is labeled with the time expressed in four digits above the line.
Bearings
It is preferable to plot true bearings, but either true or magnetic bearings can be plotted. If a relative bearing of a landmark is observed, it should be converted to true bearing by adding ship's true heading. In plotting because bearing indicates the direction of a terrestrial object from the observer, a line of position is drawn from the landmark in a reciprocal direction. If a lighthouse bears 040°, then the ship bears 220° from the lighthouse. A bearing line of position is labeled with the time expressed in four digits above the line.
A special type of bearing is the tangent. When a bearing is observed of the right edge of a projection of land, the bearing is a right tangent. If a bearing on the left edge of a projection of land, as viewed by the observer, it is a left tangent. A tangent gives an accurate line of position if the point of land is sufficiently abrupt to provide a definite point for measurement, it is inaccurate when the slope is so gradual that the point for measurement moves horizontally with the rise and fall of the tide. A distance arc is a circular line of position. When the distance from an observer to a landmark is known, the observer's position is on the circle, with the landmark as center, having a radius equal to the measured distance. The entire circle need not be drawn because in practice the navigator normally knows his position near enough that drawing an arc of a circle suffices. The arc is labeled with the time above expressed in four digits. The distance to a landmark can be measured by using radar, stadimeter, or sextant, in along with Table 9 (Green Book) of the American Practical Navigator (Bowditch).
The stadimeter is used most frequently to measure distances from your ship to others in a formation. In piloting, it also is used as a navigational instrument to ascertain distance to some navigational aid as for example, when a ship's position is being determined by bearing and distance of a fixed object of known height.
Stadimeters are of two types, the Fisk type and the Brandon sextant type. In using either type, the height of the object whose distance is desired must be known, and that height must be between 50 and 200 feet. (Usually, when measuring distances to ships the height used is from the boot topping to the top of the mast or the highest radar. Distances are measured with reasonable accuracy up to 2000 yards. Beyond that range the accuracy of the stadimeter decreases. Say you want to get the range to a 120-foot light structure. Move the carriage containing the index drum to the 120-foot mark on the index arm. Sight through the telescope at the light structure. As with the sextant, you will see a direct and a reflected image. Turning the drum causes the reflected image to move up or down relative to the direct image. When the top of the reflected image is in line with the bottom of the direct image, distance in yards can be read directly from the drum.
