CHAPTER 7 DEAD RECKONING DEFINITION AND PURPOSE
700. The Importance Of Dead Reckoning
Dead reckoning allows a navigator to determine his present position by projecting his past courses steered and speeds over ground from a known past position.He can also determine his future position by projecting an ordered course and speed of advance from a known present posi-tion.The DR position is only an approximate position because it does not allow for the effect of leeway,current, helmsman error, or gyro error.
Dead reckoning helps in determining sunrise and sunset;in predicting landfall,sighting lights and predict-ing arrival times;and in evaluating the accuracy of electronic positioning information.It also helps in pre-dicting which celestial bodies will be available for future observation.
The navigator should carefully tend his DR plot,up-date it when required,use it to evaluate external forces acting on his ship,and consult it to avoid potential naviga-tion hazards.
CONSTRUCTING THE DEAD RECKONING PLOT
Maintain the DR plot directly on the chart in use.DR at least two fix intervals ahead while piloting.If tran
siting in the open ocean,maintain the DR at least four hours ahead of the last fix position.If operating in a defined,small operating area,there is no need to extend the DR out of the operating area;extend it only to the operating area boundary.Maintaining the DR plot di-rectly on the chart allows the navigator to evaluate a vessel’s future position in relation to charted navigation hazards.It also allows the conning officer and captain to plan course and speed changes required to meet any operational commitments.
This section will discuss how to construct the DR plot. 701. Measuring Courses And Distances
To measure courses,use the chart’s compass rose near-est to the chart section currently in use.Transfer course lines to and from the compass rose using parallel rulers,rolling rulers,or triangles.If using a parallel motion plotter(PMP), simply set the plotter at the desired course and plot that course directly on the chart.
The navigator can measure direction at any convenient place on a Mercator chart because the meridians are parallel to each other and a line making an angle with any one makes the same angle with all others.Measure direction on a con-formal chart having nonparallel meridians at the meridian closest to the area of the chart in use.The only common non-conformal projection used is the gnomonic;a gnomonic chart usually contains instructions for measuring direction.
Compass roses give both true and magnetic directions. For most purposes, use true directions.
Measure distances using the chart’s latitude scale.As-suming that one minute of latitude equals one nautical mile introduces no significant error.Since the Mercator’s latitude scale expands as latitude increases,measure distances on the latitude scale closest to the area of interest.On large scale charts,such as harbor charts,use the distance scale provided. To measure long distances on small-scale charts,break the distance into a number of segments and measure each seg-ment at its mid-latitude.
Navigational computers can also compute distances be-tween two points.Because of the errors inherent in manually measuring track distances,use a navigation computer if one is available.
702. Plotting And Labeling The Course Line And Positions
Draw a new course line whenever restarting the DR.Ex-tend the course line from a fix in the direction of the ordered course.Above the course line place a capital C followed by the ordered course.Below the course line,place a capital S fol-lowed by the speed in knots.Label all course lines and fixes soon after plotting them because a conning officer or navigator can easily misinterpret an unlabeled line or position.
Enclose a fix from two or more LOPs by a small circle and label it with the time to the nearest minute.Mark a DR position with a semicircle and the time.Mark an estimated position(EP)by a small square and the time.Determining an EP is covered later in this chapter.
Express the time using four digits without punctuation. Use either zone time or GMT.
Label the plot neatly, succinctly, and clearly.
Figure702illustrates this process.The navigator plots and labels the0800fix.The conning officer orders a course
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of095°T and a speed of15knots.The navigator extends the course line from the0800fix in a direction of095°T.He calculates that in one hour at15knots he will travel15nau-tical miles.He measures15nautical miles from the0800fix position along the course line and marks that point on the course line with a semicircle.He labels this DR with the time.Note that,by convention,he labels the fix time hori-zontally and the DR time diagonally.
THE RULES OF DEAD RECKONING
703. Plotting The DR
Plot the vessel’s DR position:
1. At least every hour on the hour.
2. After every change of course or speed.
3. After every fix or running fix.
4. After plotting a single line of position.
Figure703illustrates applying these rules.Clearing the harbor at0900,the navigator obtains a last visual fix.This is taking departure,and the position determined is called the departure.At the0900departure,the conning officer orders a course of090°T and a speed of10knots.The nav-igator lays out the 090°T course line from the departure.
At1000,the navigator plots a DR position according to the rule requiring plotting a DR position at leas
t every hour on the hour.At1030,the conning officer orders a course change to060°T.The navigator plots the1030DR position in accordance with the rule requiring plotting a DR position at every course and speed change.Note that the course line changes at1030to060°T to conform to the new course.At 1100,the conning officer changes course back to090°T. The navigator plots an1100DR because of the course change,Note that,regardless of the course change,an1100 DR would have been required because of the“every hour on the hour” rule.
At1200,the conning officer changes course to180°T and speed to5knots.The navigator plots the1200DR.At 1300,the navigator obtains a fix.Note that the fix position is offset to the east from the DR position.The navigator de-termines set and drift from this offset and applies this set and drift to any DR position from1300until the next fix to determine an estimated position.He also resets the DR to the fix;that is,he draws the180°T course line from the
1300 fix, not the 1300 DR.
Figure 702. A course line with labels.
Figure 703. A typical dead reckoning plot.
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704. Resetting The DR深海导航 Reset the DR plot to the ship’s latest fix or running fix. In addition,consider resetting the DR to an inertial estimat-ed position as discussed below.
If a navigator has not received a fix for a long time,the DR plot,not having been reset to a fix,will accumulate time-dependent error.Soon that error may become so sig-nificant that the DR will no longer show the ship’s position with sufficient accuracy.If his vessel is equipped with an inertial navigator,the navigator should consider resetting the DR to the inertial estimated position.Some factors to consider when making this determination are:
(1)Time since the last fix and availability of fix infor-mation.If it has been a short time since the last fix and fix information may soon become available,it may be advis-able to wait for the next fix to reset the DR.
止痒沐浴露(2)Dynamics of the navigation situation.If,for exam-ple,a submerged submarine is operating in the Gulf Stream, fix information is available but operational considerations may preclude the submarine from going to periscope depth to obtain a fix.Similarly,a surface ship with an inertial nav-igator may be in a dynamic current and suffer a temporary loss of electronic fix equipment.In either case,the fix infor-mation will be available shortly but the dynamics of the situation call for a more accurate assessment of the vessel’s position.Plotting an inertial EP and resetting the DR to that EP may provide the navigator with a more accurate assess-ment of the navigation situation.
(3)Reliability and accuracy of the fix source.If a sub-marine is operating under the ice,for example,only the inertial EP and Omega fixes may be available for weeks at a time.Given a known inaccuracy of Omega,a high prior correlation between the inertial EP and highly accurate fix systems such as GPS,and the continued proper operation of the inertial navigator,the navigator may well decide to reset the DR to the inertial EP rather than the Omega fix.
DEAD RECKONING AND SHIP SAFETY
Properly maintaining a DR plot is important for ship safety.The DR allows the navigator to examine a future po-sition in relation to a planned track.It allows him to anticipate charted hazards and plan appropriate action to avoid them.Recall that the DR position is only approxi-mate.Using a concept called fix expansion compensates for the DR’s inaccuracy and allows the navigator to use the DR more effectively to anticipate and avoid danger.
Often a ship steams in the open ocean for extended pe-riods without a fix.This can result from of any number of factors ranging from the inability to obtain celestial fixes to malfunctioning electronic navigation systems.Infrequent fixes are particularly common on submarines.Whatever the reason,in
some instances a navigator may find himself in the position of having to steam many hours on DR alone.
The navigator must take precautions to ensure that all hazards to navigation along his path are accounted for by the approximate nature of a DR position.One method which can be used is fix expansion.
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Fix expansion takes into account possible errors in the DR calculation caused by factors which tend to affect the vessel’s actual course and speed over ground.The naviga-tor considers all such factors and develops an expanding “error circle”around the DR plot.One of the basic assump-tions of fix expansion is that the various individual effects of current,leeway,and steering error combine to cause a cumulative error which increases over time,hence,the con-cept of expansion.
Errors considered in the calculation of the fix expan-sion encompass all errors that can lead to DR inaccuracy.Some of the most important factors are current and wind, compass or gyro error,and steering error.Any method which attempts to determine an error circle must take these factors into account.The navigator can use the magnitude of set and drift calculated from his DR plot.See section707 below.He can obtain the current’s magnitude from pilot charts or weather reports.He can
determine wind speed from weather reports or direct measurement.He can deter-mine compass error by comparison with an accurate standard or by obtaining an azimuth of the sun.The naviga-tor determines the effect each of these errors has on his course and speed over ground,and applies that error to the fix expansion calculation.
As noted above,the error is a function of time;it grows as the ship proceeds down the track without a obtaining a fix.Therefore,the navigator must incorporate his calculat-ed errors into an error circle whose radius grows with time. For example,assume the navigator calculates that all the various sources of error can create a cumulative position er-ror of no more than2nm.Then his fix expansion error circle would grow at that rate;it would be2nm after the first hour, 4 nm after the second, and so on.
At what value should the navigator start this error cir-cle?Recall that a DR is laid out from every fix.All fix sources have a finite absolute accuracy,and the initial error circle should reflect that accuracy.Assume,for example, that a satellite navigation system has an accuracy of0.5nm. Then the initial error circle around that fix should be set at 0.5nm.
Construct the error circle as follows.When the navigator obtains a fix,reset the DR to that fix.Then,en
close that DR position in a circle the radius of which is equal to the accura-cy of the system used to obtain the fix.Lay out the ordered
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钉角机course and speed from the fix position.Then,apply the fix expansion circle to the hourly DR’s.In the example given above,the DR after one hour would be enclosed by a circle of radius2.5nm,after two hours4.5nm,and so on.Having encircled the four hour DR positions with the error circles, the navigator then draws two lines originating tangent to the original error circle and simultaneously tangent to the other error circles.The navigator then closely examines the area between the two tangent lines for hazards to navigation.This technique is illustrated in Figure 705 below.
The fix expansion encompasses all the area in which the vessel could be located(as long as all sources of error are con-sidered).If any hazards are indicated within the cone,the navigator should be especially alert for those dangers.If,for ex-ample,the fix expansion indicates that the vessel may be standing into shoal water,continuously monitor the fathometer. Similarly,if the fix expansion indicated that the vessel might be approaching a charted obstruction, post extra lookouts.
The fix expansion may grow at such a rate that it be-comes unwieldy.Obviously,if the fix expansion g
rows to cover too large an area,it has lost its usefulness as a tool for the navigator, and he should obtain a new fix.
DETERMINING AN ESTIMATED POSITION
An estimated position is a DR position corrected for the effects of leeway,steering error,and current.This section will briefly discuss the factors that cause the DR position to diverge from the vessel’s actual position.It will then discuss calculating set and drift and applying these values to the DR to obtain an estimated position.Finally,it will discuss deter-mining the estimated course and speed made good.
706. Factors Affecting DR Position Accuracy
Tidal current is the periodic horizontal movement of the water’s surface caused by the tide-affecting gravitation-al force of the moon.Current is the horizontal movement of the sea surface caused by meteorological,oceanograph-ic,or topographical effects.From whatever its source,the horizontal motion of the sea’s surface is an important dy-namic force acting on a vessel moving through the water. Set refers to the current’s direction,and drift refers to the current’s speed.
Leeway is the leeward motion of a vessel due to that component of the wind vector perpendicular to the vessel’s track.
Leeway and current effects combine to produce the most pronounced natural dynamic effects on a transiting vessel.
In addition to these natural forces,helmsman error and gyro error combine to produce a steering error that causes additional error in the DR.
707. Calculating Set And Drift And Plotting An Estimated Position
It is difficult to quantify the errors discussed above individually.However,the navigator can easily quantify their cumulative effect by comparing simultaneous fix and DR positions.Were there no dynamic forces acting on the vessel and no steering error,the DR position and the fix position would coincide.However,they seldom coincide.The fix is offset from the DR by a finite dis-tance.This offset is caused by the error factors discussed above.
Note again that this methodology provides no means to determine the magnitude of the individual errors.It simply provides the navigator with a measurable represen-tation of their combined effect.
Figure 705. Fix expansion. All possible positions of the ship lie between the lines tangent to the expanding circles.
Examine this area for dangers.
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When the navigator measures this combined effect,he of-ten refers to it as the “set and drift.”Recall from above that these terms technically were restricted to describing current effects.However,even th
ough the fix-to-DR offset is caused by effects in addition to the current,this text will follow the convention of referring to the offset as the set and drift.
The set is the direction from the DR to the fix.The drift is the distance in miles between the DR and the fix divided by the number of hours since the DR was last reset.This is true regardless of the number of changes of course or speed since the last fix. Calculate set and drift at every fix.
Calculate an EP by drawing from a DR position a vec-tor whose direction equals the set and whose magnitude equals the product of the drift and the number of hours since the last DR reset.See Figure 707.From the 0900DR posi-tion the navigator draws a set and drift vector.The end of that vector marks the 0900EP.Note that the EP is enclosed in a square and labeled horizontally with the time.Plot and evaluate an EP with every DR position.
708. Estimated Course And Speed Made Good
The direction of a straight line from the last fix to the EP is the estimated track made good .The length of this line divided by the time between the fix and the EP is the estimated speed made good .
Solve for the estimated track and speed by using a vec-tor diagram.See the example problems below.See.Figure 708a
Example 1:A ship on course 080°,speed 10knots,is steaming through a current having an estimated set of 140°and drift of 2 knots.电子放大镜
Required:Estimated track and speed made good.Solution:See Figure 708a.From A,any convenient point,draw AB,the course and speed of the ship,in direc-tion 080°, for a distance of 10 miles.
From B draw BC,the set and drift of the current,in di-rection 140°, for a distance of 2 miles.
Figure 707. Determining an estimated position.
Figure 708a. Finding track and speed made good through a current.
Figure 708b. Finding the course to steer at a given speed to make good a given course through a current.
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