Dead reckoning is the process of estimating your present position by projecting course and speed from a known past position. It is also used to predict a future position by projecting course and speed from a known present position.The DR position is only an approximate position because it does not allow for the effect of leeway, current, helmsman error, compass error, or other influences.
The navigator uses dead reckoning in many ways such as:
1. To determine sunrise and sunset.
2. To predict landfall, sighting lights and arrival times.
3. To evaluate the accuracy of electronic positioning information.
4. To predict which celestial bodies will be available for future observation.
The most important use of dead reckoning is to project the position of the ship into the immediate future and avoid hazards to navigation. The navigator carefully tends the DR plot, updating it when required, and uses it to evaluate external forces acting on the ship. The navigator also consults the DR plot to avoid navigation hazards. A fix taken at each DR position will reveal the effects of current, wind, and steering error, and allow the navigator to stay on track by correcting for them.
Drift: This is the speed of a current (or the speed of all offsetting influences), usually stated in knots. Some publications, such as pilot charts and atlases, express drift as nautical miles per day.
Course Made Good: CMG is the direction from a given point of departure to a subsequent position. It is the direction of the net movement from one point to another, disregarding any intermediate course changes in route. This will differ from the track if the correct allowance for current was not made.
Speed Made Good: SMG is the net speed based on distance and time of passage directly from one point to another, disregarding any intermediate speed change. SMG is speed along the CMG.
Course Over The Ground: COG is the actual path of your vessel with respect to the earth. This may differ from CMG if there are intermediate course changes, steering inaccuracies, or offsetting influences. In current sailing triangles, CMG is used.
Speed Over The Ground: SOG is your ship’s actual speed with respect to the earth along the COG. In current sailing, SMG is used.
In navigation, the word "current" includes all factors that introduce geographical error in dead reckoning. When a fix is obtained, one assumes that the current has set from the DR position at the same time as the fix and the drift equals the distance in miles between these two positions divided by the hours since the last fix. If set and drift can be estimated, a better position is obtained by applying the correction to the DR position. This is referred to as an estimated position. If a current is setting in the same direction as the course of the ship or its reciprocal, the course made good is the same, only the speed changes. If course and set are in the same direction, the speeds are added. If in opposite directions, the smaller speed is subtracted from the larger.
Leeway: is the leeward motion of a vessel due to wind. It may be expressed as distance, speed, or angular difference between the course steered and the course made good through the water. The amount of leeway depends upon the speed and relative direction of the wind, type of vessel, exposed freeboard, trim, state of the sea, and depth of water. Leeway is most conveniently applied by adding its effect to that of the current and other elements introducing geographical error in the dead reckoning.
Time, Speed and Distance: All piloting and maneuvering solutions contain three factors: time, speed, and distance. When piloting you should be able to figure in your head any one of the three factors. The following are two simple methods that you can use.
The 3 Minute Rule: This is an excellent method for computing time, speed, and or distance, when working in an area where short distances are involved or the times between measurements are close together. The 3 minute rule is: the distance, in yards, traveled by a ship in 3 minutes is equal to the speed of the ship multiplied by 100.
Example 2: A ship’s speed is 15 knots. How far will it travel in 3 minutes?
D = S x 100 = 15 x 100 = 1500 yards
When you have determined the distance traveled in 3 minutes, you can determine the distance traveled in 1 minute by dividing the distance by 3.
The 60 Minute Rule: This method for computing time, speed, or distance requires that you know two factors in order to determine the third.
Piloting: Is a method of determining position and directing the movements of your vessel by reference to landmarks, navigational aids, or soundings. Piloting is usually used as a primary means of navigation when entering or leaving port and in coastal navigation. In piloting, the navigator obtains warnings of danger, fixes the position frequently and accurately, and determines the proper course of action.
Lines of Position: A LOP is a line at some point of which a ship may be presumed to be on, as a result of observation or measurement. When piloting, LOPs are used to fix a ship’s position. An LOP is determined with reference to a landmark, which must be correctly identified, and its position must be shown on your chart. There are three general types of LOPs, ranges, bearings, tangents, and distance arcs.
A ship is on "range" when two landmarks are observed in line. This range is represented on a chart by means of a straight line which if extended would pass through the two related chart symbols. This line is labeled with the time expressed in four digits (above the line), is a fix of the ship’s position. It is better to plot true bearings, but either true or magnetic bearings may be plotted. When the relative bearing of a landmark is observed it should be converted to true bearing or direction by the addition of the ship’s true heading. Since a bearing indicates the direction of a terrestrial object from the observer, a LOP is plotted from the landmark in a reciprocal direction. For example, if a lighthouse bears 300°, the ship bears 120° from the lighthouse. A bearing LOP is labeled with the time expressed in four digits above the line and the bearing in three digits below the line.
A special type of bearing is the tangent: When a bearing is observed on the right hand edge of a projection of land, the bearing is a right tangent. A bearing on the left-hand edge of a projection of land as viewed by the observer is a left tangent. A tangent provides an accurate LOP if the point of land is sufficiently abrupt to provide a definite point for measurement. A distance arc is a circular LOP: When the distance from an observer to a landmark is known, the fix of the observer’s position is a circle with the landmark as center having a radius equal to the distance. The entire circle need not be drawn, since in practice the navigator normally knows his position with sufficient accuracy as to require only the drawing of an arc of a circle. The arc is labeled with the time above expressed in four digits and the distance below in nautical miles (and tenths). The distance to a landmark may be measured using radar, the stadimeter, or the sextant in along with Tables 9 and 10 of the American Practical Navigator.
Fixes: A fix is defined as a point of intersection of two or more simultaneously obtained LOPs. The symbol for a fix is a small circle around the point of intersection. It is labeled with the time expressed in four digits. Fixes may be obtained using the following combinations of LOPs:
A line of bearing or tangent and a distance arc.
Two or more lines of bearing or tangents.
Two or more distance arcs.
Two or more ranges.
A range and a line of bearing or tangent.
A range and a distance arc.
Since two circles may intersect at two points, two distance arcs used to obtain a fix are not undesirable. The navigator in making his choice between two points of intersection must consider an approximate bearing, sounding, or your DR position. When a distance arc of one landmark and a bearing of another are used, the navigator may again be faced with the problem of choosing between two points of intersection at the same location.
Selecting Landmarks: Three considerations in selecting landmarks or other aids for obtaining LOPs are:
1. Angle of intersection.
2. Number of objects.
3. Permanency.
Two LOPs crossing at nearly right angles will result in a fix with a smaller amount of error than two LOPs separated by less than 30° . If there is a small compass error or a slight error is made in reading the bearings, the resulting discrepancy will be less in the case of the fix produced by widely separated LOPs than the fix from LOPs separated by only a few degrees. If only two landmarks are used, any error in observation or identification may not be apparent. With three or more LOPs, each LOP acts as a check. If all intersect in a pinpoint or form a small triangle, you may generally rely on the fix. Where three LOPs are used, a spread of 60° would result in a better accuracy.
When selecting landmarks or other aids, preference should be given to permanent structures such as lighthouses or other structural and natural features identifiable ashore or in shallow water. Buoys are very convenient, but less permanent and may drift from their charted position because of weather and sea conditions. Sometimes a navigator has no choice of landmarks or their permanency, number, or spread. In these cases you must use whatever is available, no matter how undesirable. In the evaluation of your fix, the number of landmarks, their permanency, and their spread should receive consideration. When three LOPs cross forming a triangle, it is difficult to determine whether the triangle is the result of a compass error or an erroneous LOP. The plotting of four LOPs usually indicates if a LOP is in error.
Running Fix: It is not always possible for the navigator to observe LOPs simultaneously. Sometimes only one landmark is available. The navigator may make frequent observations of the one landmark, or you might, after one observation, lose sight of the available landmark only to sight a new navigational aid. If the navigator is able to compute distances during these observations, you may easily establish your fix. If not, or if for any reason your data consists of LOPs obtained at different times, then you may establish a position that only partially takes into account the current. This position is the running fix, identified by the same symbol as the fix except that the time label is followed by the abbreviation "R. FIX." It is better than a DR position, but less desirable than a fix.
A running fix is established by advancing the first LOP in the direction of travel of the ship (the course), a distance equal to the nautical miles the ship should have traveled during the interval between the time of the first LOP and the time of the second LOP. The point of intersection of the first LOP as advanced and the second LOP is the running fix. The advanced LOP is labeled with the times of the two LOPs separated by a dash and the direction, above and below the line.
Use one of the following methods if the ship changes course and or speed between observations:
Perpendicular Method: After two LOPs are obtained, plot DR positions corresponding to the lines of the LOPs. Drop a perpendicular from the earlier DR to the earlier LOP. At the second DR, make a line having the same direction and length as the first perpendicular. At the end of the line, make a line parallel to the original LOP (this is the advanced LOP). The intersection of this advanced LOP and the last observed LOP establishes the running fix. The following is the logic of the perpendicular method. The ship's speed and course generates the DR track line. If the advanced LOP lies with respect to the second DR position as it previously lay with respect to the old DR, then it has been advanced parallel to itself a distance and a direction consistent with the ship’s movement during the intervening time. A variation of this method is to construct, instead of a perpendicular, a line of any direction between the first DR and LOP. This line is then duplicated at the second DR and the LOP advance as before. In duplication, the line from the second DR must be the same length and direction as the line connecting the first DR and LOP.
Course Made Good: As in the perpendicular method, plot DR positions to match the time labels of the LOPs. Connect the DR positions. The connecting line represents the course and distance that the ship should have made good. Advance the first LOP a distance and direction corresponding to the line connecting the two DR positions.
Running Fix Considerations: The running fix may be a well-determined position and is usually considered as such. For this reason the DR track is normally replotted using the running fix as a new point of origin. A running fix does not fully account for current, and the displacement of the running fix from the DR is not a true indication of current. If a head current is expected, extra allowance should be made for clearance of dangers to be passed abeam, because the plot of running fixes based upon any single landmark near the beam will indicate the ship to be farther from that danger than it actually is. If a following current is experienced, then the opposite condition will exist. This happens because the actual distance made good is less with a head current and greater with a following current than the distance the LOP is advanced based upon dead reckoning. A limitation of 30 minutes should be used on the elapsed time between LOPs in a running fix.
Determining your Position by Soundings: A position obtained by sounding is usually approximate. Accuracy of this type of position depends on the following: How completely and accurately depths are indicated on the chart. The irregularity of the depths.
It is impossible to obtain a position by soundings if the ship is located in an area where depth is the same throughout. In practice, position by soundings serves as a check on a fix taken by some other means. Suppose you have only one spot on or near your DR track where water depth is 6 fathoms and the depth over the rest of the area for miles around is 20 fathoms. If you record 6 fathoms, you can be certain you are located at the one point where a 6-fathom depth was shown on the chart.
Piloting by soundings is not that simple. What you really do is get a contour of the bottom you are passing over and try to match it up with a similar contour shown by the depth figures on the chart. One of the best methods is to proceed as follows: Draw a straight line on a piece of transparent paper or plastic. Calculate how far apart your soundings will be, in other words, the length of the ship’s run between soundings and mark off distances on the line to the scale of the chart. Alongside each mark representing a sounding, record the depth obtained at that sounding. The line represents the ship’s course. The line of soundings recorded on the overlay should fit the depth marks on the chart somewhere near your DR track. If it makes an accurate fit, it probably is a close approximation of the course the ship is actually making good.
