Piloting: Bearings, Distance Off and Dead Reckoning

Dead reckoning (DR) is a method for determining the estimated position of a vessel by advancing from a known fix of position along the vessel’s ordered course and speed. This can be used to determine where a vessel currently is or where it will be. This is an approximate position; it does not allow for the many errors that can cause a vessel to veer off course such as helmsmen error, compass error, or current and wind.

Dead reckoning helps in predicting landfall, determining distances to objects, predicting arrival times, and evaluating the accuracy of electronic positioning information. It also aids in predicting which celestial bodies will be available for future observation. However, its most important use is in projecting the ship's position in the immediate future and avoiding hazards to navigation.

The navigator should carefully tend his or her DR plot, updating it when required and using it to evaluate external forces acting on his or her ship. Navigators can compare the dead reckoning position to a known fix to determine other forces acting on the vessel, such as wind and current. They can then use all this information to create a more accurate DR plot and stay on course by correcting for the known errors and their effects.

The use of DR when an Electronic Chart Display and Information System (ECDIS) is the primary plotting method can vary with the type of system. An ECDIS can display the ship's heading projected out to show future positions as a function of time, display waypoint information, and/or show progress toward each waypoint in turn.

Presently, marine navigation is in a time of transition with some ships completely paperless and others using a combination of electronic and paper charting. If paper charts are the back up to ECDIS (instead of an additional type-approved ECDIS) it would be prudent to DR as a cross-check to the GPS/GNSS derived position on the ECDIS. Plotting positions on the paper chart should be done at appropriate intervals. The following procedures apply to DR plotting on the traditional paper chart.

The DR plot should be maintained directly on the chart in use. DR at least two fix intervals ahead while piloting. When transiting on the open ocean, maintain the DR at least four hours ahead of the last fix position. Maintaining the DR plot directly 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.

To measure courses, use the chart’s compass rose nearest to the chart area 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. Transparent plastic navigation plotters that align with the latitude/longitude grid may also be used.

The navigator can measure direction at any convenient place on a Mercator chart. All the meridians are parallel to each other and a line making an angle with any one makes the same angle with all others. When measuring direction on a conformal chart having nonparallel meridians, use the meridian closest to the area of the chart in use. A common nonconformal projection used is the gnomonic; a gnomonic chart usually contains instructions for measuring direction.

Compass roses may give both true and magnetic directions. True directions are on the outside of the rose; magnetic directions are on the inside. For most purposes, use true directions.

Measure distances using the chart's latitude scale. Although not technically true, assuming that one minute of latitude equals one nautical mile introduces no significant error. The latitude scale on a Mercator chart expands as the latitude increases, therefore one must measure distances on the latitude scale closest to the area of interest when working with small-scale charts. On large-scale charts, such as harbor charts, one can use either the latitude scale or the distance scale provided. To measure long distances on small-scale charts, break the distance into a number of segments and measure each segment at its mid-latitude.

Draw a new course line whenever restarting the DR. To draw a DR, extend 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 in degrees true. Below the course line, place a capital S followed by the speed in knots. Label all course lines and fixes after plotting them because a conning officer or navigator can easily misinterpret an unlabeled line or position.

Enclose a fix from two or more Lines of Position (LOP) by a small circle and label it with the time to the nearest minute, written horizontally. Mark a DR position with a semicircle and the time, written diagonally. Mark an estimated position (EP) by a small square and the time, written horizontally. Determining an EP is covered later in this chapter.

Express the time using four digits without punctuation, using either zone time or Greenwich Mean Time (GMT), according to procedure. Label the plot neatly, succinctly,

[Figure 1002 in Bowditch, Pub. No. 9: A course line with labels.]

Figure 1002 illustrates this process. The navigator plots and labels the 0800 fix. The conning officer orders a course of 095°T and a speed of 15 knots. The navigator extends the course line from the 0800 fix in a direction of 095°T. S/He calculates that in one hour at 15 knots he will travel 15 nautical miles. S/He measures 15 nautical miles from the 0800 fix position along the course line and marks that point on the course line with a semicircle. S/He labels this DR with the time. Note that, by convention, he labels the fix time horizontally and the DR time diagonally.

To effectively maintain the vessel’s DR position, the navigator must follow the 4 rules of 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.

Figure 1003 illustrates applying these rules. Clearing the harbor at 0900, the navigator obtains a last visual fix. This is called taking departure, and the position determined is called the departure. At the 0900 departure, the conning officer orders a course of 090°T and a speed of 10 knots. The navigator lays out the 090°T course line from the departure.

At 1000, the navigator plots a DR position according to the rule requiring plotting a DR position at least every hour on the hour. At 1030, the conning officer orders a course change to 060°T. The navigator plots the 1030 DR position in accordance with the rule requiring plotting a DR position at every course and speed change. Note that the course line changes at 1030 to 060°T to conform to the new course. At 1100, the conning officer changes course back to 090°T. The navigator plots an 1100 DR due to the course change. Note that, regardless of the course change, an 1100 DR would have been required because of the “every hour on the hour” rule.

At 1200, the conning officer changes course to 180°T and speed to 5 knots. The navigator plots the 1200 DR. At 1300, the navigator obtains a fix. Note that the fix position is offset to the east from the DR position. The navigator determines set and drift from this offset and applies this set and drift to any DR position from 1300 until the next fix to determine an estimated position. S/He also resets the DR to the fix; that is, s/he draws the 180°T course line from the 1300 fix, not the 1300 DR.

Reset the DR plot to each fix or running fix in turn. In addition, consider resetting the DR to an inertial estimated position, if an inertial system is installed.

If a navigator has not taken a fix for an extended period of time, the DR plot, not having been reset to a fix, will accumulate time-dependent errors. Over time that error may become so significant that the DR will no longer show the ship’s position with acceptable accuracy. If the vessel is equipped with an inertial navigator, the navigator should consider resetting the DR to the inertial estimated position. Some factors to consider when determining whether to reset the DR are:

(1) Time since the last fix and availability of fix information. If it has been a short time since the last fix and fix information may soon become available, it may be advisable to wait for the next fix to reset the DR.

(2) Dynamics of the navigation situation. If, for example, 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

[Figure 1003 in Bowditch, Pub. No. 9: A typical dead reckoning plot.]

to obtain a fix. Similarly, a surface ship with an inertial navigator may be in a dynamic current and suffer a temporary loss of electronic fix equipment. In either case, the fix information 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 assessment of the navigation situation.

(3) Reliability and accuracy of the fix source. If a submarine is operating under the ice, for example, only the inertial EP fixes may be available for weeks at a time. Given 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 decide to reset the DR to the inertial EP.

Properly maintaining a DR plot is important for ship safety. The DR allows the navigator to examine a future position 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 approximate. 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.

Circumstances may arise where a ship steams in the open ocean for extended periods without a fix. This can result from a combination 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.

Navigators must take precautions to ensure that all hazards to navigation along their path are accounted for by the approximate nature of a DR position. One method which can be used is fix expansion.

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 the ground. The navigator considers all such factors and develops an expanding “error circle” around the DR plot. One of the basic assumptions 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 concept of expansion. While the errors may in fact cancel each other out, the worst case is that they will all be additive, and this is what the navigator must anticipate.

Errors considered in the calculation of fix expansion 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 or her DR plot. See Section 1007. The current's estimated magnitude can be obtained from pilot charts or weather reports. Wind speed can be gathered from weather instruments. Compass error can be found by comparison with an accurate standard or by obtaining an azimuth of the Sun. The navigator determines the effect each of these errors has on his of her course and speed over ground, and applies that error to the fix expansion calculation.

As noted previously, error is a function of time; it grows as the ship proceeds along the track without obtaining a fix. Therefore, the navigator must incorporate the calculated errors into an error circle whose radius grows with time. For example, assume the navigator calculates that all

[Figure 1005 in Bowditch, Pub. No. 9: Fix expansion. All possible positions of the ship lie between the lines tangent to the expanding circles. Examine this area for dangers.]

the various sources of error can create a cumulative position error of no more than 2 nm. Then his or her fix expansion error circle would grow at that rate; it would be 2 nm after the first hour, 4 nm after the second, and so on.

At what value should the navigator start this error circle? 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 of 0.5 nm. Then the initial error circle around that fix should be set at 0.5 nm.

First, enclose the fix position in a circle, the radius of which is equal to the accuracy of the system used to obtain the fix. Next, lay out the ordered course and speed from the fix position. Then apply the fix expansion circle to the hourly DRs, increasing the radius of the circle by the error factor each time. In the example given above, the DR after one hour would be enclosed by a circle of radius 2.5 nm (that is, 2 nm of cumulative position error + 0.5 nm of satellite navigation error), after two hours 4.5 nm, 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 1005.

The fix expansion encompasses the total area in which the vessel could be located (as long as all sources of error are considered). If any hazards are indicated within the cone, the navigator should be especially alert for those dangers. If, for example, the fix expansion indicates that the vessel may be standing into shoal water, continuously monitor the fathometer. Similarly, if the fix expansion indicates that the vessel might be approaching a charted obstruction, post extra lookouts.

The fix expansion may grow at such a rate that it becomes unwieldy. Obviously, if the fix expansion grows to cover too large an area, it has lost its usefulness as a tool for the navigator, and he or she should obtain a new fix by any available means.

An estimated position (EP) 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. It will also discuss determining the estimated course and speed made good.

Tidal current is the periodic horizontal movement of the sea caused by the tide-affecting gravitational forces of the moon and sun. Current is the horizontal movement of the sea caused by meteorological, oceanographic, or topographical effects. From whatever its source, the horizontal motion of the sea is an important dynamic force acting on a vessel.

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 combine to produce the most pronounced natural dynamic effects on a transiting vessel. Leeway especially affects sailing vessels and high-sided vessels.

In addition to these natural forces, relatively small helmsman and steering compass errors may combine to cause additional error in the DR.

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. If there are no dynamic forces acting on the vessel and no steering error, the DR position and the fix position will coincide. However, this seldom occurs; the fix is normally offset from the DR by the vector sum of all the errors.

Note again that this methodology provides no means to determine the magnitude of the individual errors. It simply provides the navigator with a measurable representation of their combined effect.

When the navigator measures this combined effect, s/he often refers to it as the “set and drift.” Recall from above that these terms technically were restricted to describing current effects. However, even though 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. The prudent navigator calculates set and drift at every fix.

To calculate an EP, draw a vector from the DR position in the direction of the set, with the length equal to the product of the drift and the number of hours since the last reset. See Figure 1007. From the 0900 DR position the navigator draws a set and drift vector. The end of that vector marks the 0900 EP. Note that the EP is enclosed in a square and labeled horizontally with the time. Plot and evaluate an EP with every DR position.

[Figure 1007 in Bowditch, Pub. No. 9: Determining an estimated position.]

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 vector diagram. See the example problems below and refer to Figure 1008a. Example 1: A ship on course 080°, speed 10 knots, is steaming through a current having an estimated set of 140° and drift of 2 knots. Required: Estimated track and speed made good. Solution: See Figure 1008a. From A, any convenient point, draw AB, the course and speed of the ship, in direction 080°, for a distance of 10 miles. From B draw BC, the set and drift of the current, in direction 140°, for a distance of 2 miles. The direction and length of AC are the estimated track and speed made good. Answers: Estimated track made good 089°, estimated speed made good 11.2 knots.

To find the course to steer at a given speed to make good a desired course, plot the current vector from the origin, A, instead of from B. See Figure 1008b. Example 2: The captain desires to make good a course of 095° through a current having a set of 170° and a drift of 2.5 knots, using a speed of 12 knots. Required: The course to steer and the speed made good. Solution: See Figure 1008b. From A, any convenient point, draw line AB extending in the direction of the course to be made good, 095°. From A draw AC, the set and drift of the current. Using C as a center, swing an arc of radius CD, the speed through the water (12 knots), intersecting line AB at D. Measure the direction of line CD, 083.5°. This is the course to steer. Measure the length AD, 12.4 knots. This is the speed made good. Answers: Course to steer 083.5°, speed made good 12.4 knots.

[Figure 1008a in Bowditch, Pub. No. 9: Finding track and speed made good through a current.]

[Figure 1008b in Bowditch, Pub. No. 9: Finding the course to steer at a given speed to make good a given course through a current.]

[Figure 1008c in Bowditch, Pub. No. 9: Finding course to steer and speed to use to make good a given course and speed through the current.]

To find the course to steer and the speed to use to make good a desired course and speed, proceed as follows: See Figure 1008c. Example 3: The captain desires to make good a course of 265° and a speed of 15 knots through a current having a set of 185° and a drift of 3 knots. Required: The course to steer and the speed to use. Solution: See Figure 1008c. From A, any convenient point, draw AB in the direction of the course to be made good, 265° and for length equal to the speed to be made good, 15 knots. From A draw AC, the set and drift of the current. Draw a straight line from C to B. The direction of this line, 276°, is the required course to steer; and the length, 14.8 knots, is the required speed. Answers: Course to steer 276°, speed to use 14.8 knots.

Piloting involves navigating a vessel in restricted waters and fixing its position as precisely as possible at frequent intervals. Proper preparation and attention to detail are more important here than in other phases of navigation. This chapter will discuss a piloting methodology designed to ensure that procedures are carried out safely and efficiently. These procedures will vary from vessel to vessel according to the skills and composition of the piloting team. It is the responsibility of the navigator to choose the procedures applicable to his or her own situation, to train the piloting team in their execution, and to ensure that duties are carried out properly.

These procedures are written primarily from the perspective of the military navigator, with some notes included where civilian procedures might differ. This set of procedures is designed to minimize the chance of error and maximize safety of the ship.

The military navigation team will nearly always consist of several more people than are available to the civilian navigator. Therefore, the civilian navigator must streamline these procedures, eliminating certain steps, doing only what is essential to keep his or her ship in safe water.

The navigation of civilian vessels will therefore proceed differently than for military vessels. For example, while the military navigator might have bearing takers stationed at the gyro repeaters on the bridge wings for taking simultaneous bearings, the civilian navigator must often take and plot them himself. While the military navigator will have a bearing book and someone to record entries for each fix, the civilian navigator will simply plot the bearings on the chart as they are taken and not record them at all.

ECDIS is a good instrument to monitor the vessels track, however, the prudent navigator should continue to actively plot positions. If a pilot is aboard, as is often the case in the most restricted of waters, his or her judgment can generally be relied upon explicitly, further easing the workload. But should the ECDIS fail, the navigator will have to rely on his or her skill in the manual and time-tested procedures discussed in this chapter.

While an ECDIS is the legal equivalent of a paper chart and can be used as the primary plot, an ECS, (non-SOLAS compliant electronic chart system) cannot be so used. An ECS may be considered as an additional resource used to ensure safe navigation, but cannot be relied upon for performing all the routine tasks associated with piloting. The individual navigator, with knowledge of his or her vessel, his or her crew, and the capabilities they possess, must make a professional judgment as to how the ECS can support his or her efforts to keep his or her ship in safe water. The navigator should always remember that reliance on any single navigation system courts disaster. An ECS does not relieve the navigator of maintaining a proper and legal plot on a paper chart.

The navigator’s job begins well before getting underway. Advance preparation is necessary to ensure a safe and efficient voyage. The following steps are representative:

Ensure the plotting station(s) have the following instruments:

Dividers: Dividers are used to measure distances •

between points on the chart.

Compasses: Compasses are used to plot range arcs for •

radar LOP’s. Beam compasses are used when the

range arc exceeds the spread of a conventional com-

pass. Both types should be available at the plotting sta-

tions.

Plotters: Several types of plotters are available. The •

preferred device for large vessels is the parallel motion

plotter (PMP) used in conjunction with a drafting table.

Otherwise, use a transparent protractor plotter, or trian-

gles, parallel rulers or rolling rulers in conjunction with

the chart’s compass rose. Finally, the plotter can use a

one arm protractor. The plotter should use the device

with which he or she can work the most quickly and

accurately.

Sharpened Pencils and Erasers: Ensure an adequate •

supply of pencils is available.

Nautical Slide Rule: For solving time, speed, and dis- •

tance problems.

Tide and Current Graphs: Post the tide and current •

graphs near the primary plot for easy reference during

the transit. Give a copy of the graphs to the conning

officer and the captain.

Once the navigator verifies the above equipment is in place, he or she tapes down the charts on the chart table. If more than one chart is required for the transit, tape the charts in a stack such that the plotter works from the top to the bottom of the stack. This minimizes the time required to shift the chart during the transit. If the plotter is using a PMP, align the arm of the PMP with any meridian of longitude on the chart. While holding the PMP arm stationary, adjust the PMP to read 000.0°T. This procedure calibrates the PMP to the chart in use. Perform this alignment every time the piloting team shifts charts.

Be careful not to fold under any important information when folding the chart on the chart table. Ensure the chart’s distance scale, the entire track, and all important warning information are visible.

Energize and test all electronic navigation equipment, if not already in operation. This includes the radar and the GPS receiver. Energize and test the fathometer. Ensure the entire electronic navigation suite is operating properly prior to entering restricted waters.

Assemble or Download Required Publications. •

These publications should include Coast Pilots, Sail-

ing Directions, USCG Light Lists, NGA Lists of Lights,

Tide Tables, Tidal Current Tables, Notice to Mariners,

and Local Notice to Mariners. Often, for military ves-

sels, a port will be under the operational direction of a

particular squadron; obtain that squadron’s port Oper-

ation Order. Civilian vessels should obtain the port’s

harbor regulations. These publications will cover local

regulations such as speed limits and bridge-to-bridge

radio frequency monitoring requirements. Assemble

and review the Broadcast Notice to Mariners file.

Select and Correct Charts. Choose the largest scale •

chart available for the harbor approach or departure.

Often, the harbor approach will be too long to be rep-

resented on only one chart. For example, three charts

are required to cover the waters from the Naval Station

in Norfolk to the entrance of the Chesapeake Bay.

Therefore, obtain all the charts required to cover the

entire passage. Using the Notice to Mariners, verify

that these charts have been corrected through the latest

Notice to Mariners. Check the Local Notice to Mari-

ners and the Broadcast Notice to Mariners file to

ensure the chart is fully corrected. Annotate on the

chart or a chart correction card all the corrections that

have been made; this will make it easier to verify the

chart’s correction status prior to its next use. Naval

ships may need to prepare three sets of charts. One set

is for the primary plot, the second set is for the second-

ary plot, and the third set is for the conning officer and

captain. Civilian vessels will prepare one set.

Mark the Minimum Depth Contour: Determine the •

minimum depth of water in which the vessel can safely

operate and outline that depth contour on the chart. Do

this step before doing any other harbor navigation

planning. Highlight this outline in a bright color so that

it clearly stands out. Carefully examine the area inside

the contour and mark the isolated shoals less than the

minimum depth which fall inside the marked contour.

Determine the minimum depth in which the vessel can

operate as follows:

Minimum Depth = Ship’s Draft – Height of Tide +

Safety Margin + Squat. (See Section 1104 and Section

1118.)

Remember that often the fathometer’s transducer is not

located at the section of the hull that extends the fur-

thest below the waterline. Therefore, the indicated

depth of water is that below the fathometer transducer,

not the depth of water below the vessel’s deepest draft.

Highlight Selected Visual Navigation Aids •

(NAVAIDS). Circle, highlight and label the main nav-

igational aids on the chart. Consult the applicable

Coast Pilot or Sailing Directions to determine a port’s

best NAVAIDS if the piloting team has not visited the

port previously. These aids can be lighthouses, piers,

shore features, or tanks; any prominent feature that is

displayed on the chart can be used as a NAVAID.

Label critical buoys, such as those marking a harbor

entrance or a traffic separation scheme. Verify charted

lights against the Light List or the List of Lights to con-

firm the charted information is correct. This becomes

most critical when attempting to identify a light at

night. Label NAVAIDS succinctly and clearly. Ensure

everyone in the navigation team refers to a NAVAID

using the same terminology. This will reduce confu-

sion between the bearing taker, the bearing recorder,

and plotter.

Highlight Selected Radar NAVAIDS. Highlight •

radar NAVAIDS with a triangle instead of a circle. If

the NAVAID is suitable for either visual or radar pilot-

ing, it can be highlighted with either a circle or a trian-

gle.

Plot the Departure/Approach Track. This process is •

critical for ensuring safe pilotage. Consult the Fleet

Guide and Sailing Directions for recommendations on

the best track to use. Look for any information or reg-

ulations published by the local harbor authority. Lack-

ing any of this information, locate a channel or safe

route on the chart and plot the vessel’s track. Most U.S.

ports have well-defined channels marked with buoys.

Carefully check the intended track to ensure a suffi-

cient depth of water under the keel will exist for the

entire passage. If the scale of the chart permits, lay the

track out to the starboard side of the channel to allow

for any vessel traffic proceeding in the opposite direc-

tion. Many channels are marked by natural or man-

made ranges. The bearings of these ranges should be

measured to the nearest 0.1° or noted from the Light

List, and this value should be marked on the chart. Not

only are ranges useful in keeping a vessel on track, they

are invaluable for determining gyro error. See Section

1107.

[Figure 1102a in Bowditch, Pub. No. 9: Turning circle.]

Label the Departure/Approach Track. Label the •

track course to the nearest 0.5°. Similarly, label the dis-

tance of each track leg. Highlight the track courses for

easy reference while piloting. Often a navigator might

plan two separate tracks, for use during good visibility

and the other for poor visibility. Considerations might

include concern for the number of turns (fewer turns

for poor visibility) or proximity to shoal water (smaller

margin for error might be acceptable in good visibil-

ity). In this case, label both tracks as above and appro-

priately mark when to use each track.

Use Advance and Transfer to Find Turning Points. •

The distance the vessel moves along its original course

from the time the rudder is put over until the new

course is reached is called advance. The distance the

vessel moves perpendicular to the original course

during the turn is called transfer. The track determined

above does not account for these. See Figure 1102b.

Use the advance and transfer characteristics of the ves-

sel to determine when the vessel must put its rudder

over to gain the next course. From that point, fair in a

curve between the original course and the new course.

Mark the point on the original course where the vessel

must put its rudder over as the turning point. See Fig-

ure 1102c.

[Figure 1102b in Bowditch, Pub. No. 9: Advance and transfer.]

Plot Turn Bearings and Ranges. A turn bearing •

is a predetermined bearing to a charted object from

the track point at which the rudder must be put over

in order to make a desired turn. In selecting a

NAVAID for a turn bearing, find one as close to

abeam as possible at the turning point, and if pos-

sible on the inside elbow of the turn. Account for

advance and transfer and label the bearing to the

nearest 0.1°. A turn range is similar, but taken as a

radar range to a prominent object ahead or astern.

Ideally, both can be used, one as a check against the

other. Example: Figure 1102c illustrates using advance and transfer to determine a turn bearing. A ship proceeding on course 100° is to turn 60° to the left to come on a range which will guide it up a channel. For a 60° turn and the amount of rudder used, the advance is 920 yards and the transfer is 350 yards. Required: The bearing of flagpole “FP.” when the rudder is put over.

[Figure 1102c in Bowditch, Pub. No. 9: Allowing for advance and transfer.]

Solution:

1. Extend the original course line, AB.

2. At a perpendicular distance of 350 yards, the trans-

fer, draw a line A'B' parallel to the original course

line AB. The point of intersection, C, of A'B' with

the new course line is the place at which the turn is

to be completed.

3. From C draw a perpendicular, CD, to the original

course line, intersecting at D.

4. From D measure the advance, 920 yards, back

along the original course line. This locates E, the

point at which the turn should be started.

5. The direction of “FP.” from E, 058°, is the bearing

when the turn should be started. Answer: Bearing 058°.

Plot a Slide Bar for Every Turn Bearing: If the ship •

is off track immediately prior to a turn, a plotting tech-

nique known as the slide bar can quickly revise a turn

bearing. See Figure 1102d. A slide bar is a line drawn

parallel to the new course through the turning point on

the original course. The navigator can quickly deter-

mine a new turn bearing by dead reckoning ahead from

the vessel’s last fix position to where the DR intersects

the slide bar. The revised turn bearing is simply the

bearing from that intersection point to the turn bearing

NAVAID. Draw the slide bar with a different color

from that used for the track in order to see the slide bar

clearly.

Label Distance to Go from Each Turn Point: At •

each turning point, label the distance to go until either

the ship moors (inbound) or the ship clears the harbor

(outbound). For an inbound transit, a vessel’s captain is

usually more concerned about time of arrival, so

assume a speed of advance and label each turn point

with time to go until mooring.

Plot Danger Bearings: Danger bearings warn a navi- •

gator s/he may be approaching a navigational hazard

too closely. See Figure 1102e. Vector AB indicates a

vessel’s intended track. This track passes close to the

indicated shoal. Draw a line from the NAVAID H tan-

gent to the shoal. The bearing of that tangent line mea-

sured from the ship’s track is 074.0°T. In other words,

as long as NAVAID H bears less than 074°T as the

vessel proceeds down its track, the vessel will not

ground on the shoal. Hatch the side of the bearing line

on the side of the hazard and label the danger bearing

NMT (no more than) 074.0°T. For an added margin of

safety, the line does not have to be drawn exactly tan-

gent to the shoal. Perhaps, in this case, the navigator

might want to set an error margin and draw the danger

bearing at 065°T from NAVAID H. Lay down a danger

bearing from any appropriate NAVAID in the vicinity

[Figure 1102d in Bowditch, Pub. No. 9: The slide bar technique.]

[Figure 1102e in Bowditch, Pub. No. 9: A danger bearing, hatched on the dangerous side, labeled with the appropriate bearing.]

of any hazard to navigation. Ensure the track does not

cross any danger bearing.

Plot Danger Ranges: The danger range is analogous •

to the danger bearing. It is a standoff range from an

object to prevent the vessel from approaching a hazard

too closely.

Label Warning and Danger Soundings: To deter- •

mine the danger sounding, examine the vessel’s pro-

posed track and note the minimum expected sounding.

The minimum expected sounding is the difference

between the shallowest water expected on the transit

and the vessel’s maximum draft. Set 90% of this differ-

ence as the warning sounding and 80% of this differ-

ence as the danger sounding. The captain may require

lower margins. There may be peculiarities about local

conditions or forecast wave and swell that will cause

the navigator to choose another method of setting

warning and danger soundings. Use the above method

if no other means is more suitable. For example: A ves-

sel draws a maximum of 20 feet, and it is entering a

channel dredged to a minimum depth of 50 feet. Set the

warning and danger soundings at 0.9 (50ft. - 20ft) =

27ft and 0.8 (50ft. - 20ft.) = 24ft., respectively. Re-

evaluate these soundings at different intervals along

the track, when the minimum expected sounding may

change. Carefully label the points along the track

between which these warning and danger soundings

apply.

Label Air Draft: Label the minimum height for •

bridges and other height restrictions.

Label Demarcation Line: Clearly label the point on •

the ship’s track where the Inland and International

Rules of the Road apply. This is applicable only when

piloting in U.S. ports.

Mark Speed Limits Where Applicable: Often a har- •

bor will have a local speed limit in the vicinity of piers,

other vessels, or shore facilities. Mark these speed lim-

its and the points between which they are applicable on

the chart.

Mark the Point of Pilot Embarkation: Some ports •

require vessels over a certain size to embark a pilot. If

this is the case, mark the point on the chart where the

pilot is to embark.

Mark the Tugboat Rendezvous Point: If the vessel •

requires a tug to moor, mark the tug rendezvous point

on the chart.

Mark the Chart Shift Point: If more than one chart •

will be required to complete the passage, mark the

point where the navigator should shift to the next chart.

Harbor Communications: Mark the point on the •

chart where the vessel must contact harbor control.

Also mark the point where a vessel must contact its

parent squadron to make an arrival report (military ves-

sels only).

Tides and Currents: Mark the points on the chart for •

which the tides and currents were calculated.

Ensure the following records are assembled and personnel assigned to maintain them:

Bearing Record Book: The bearing recorders for the •

primary and secondary plots should record all the bear-

ings used on their plot during the entire transit. The

books should clearly list what NAVAIDS are being

used and what method of navigation was being used on

their plot. In practice, the primary bearing book will

contain mostly visual bearings and the secondary bear-

ing book will contain mostly radar ranges and bearings.

Fathometer Log: In restricted waters, monitor sound- •

ings continuously and record soundings every five

minutes in the fathometer log. Record all fathometer

settings that could affect the sounding display.

Deck Log: This log is the legal record of the passage. •

Record all ordered course and speed changes. Record

all the navigator’s recommendations and whether the

navigator concurs with the actions of the conning offi-

cer. Record all buoys passed, and the shift between

international and inland Rules of the Road. Record the

name and embarkation of any pilot. Record who has

the conn at all times. Record any casualty or important

event. The deck log combined with the bearing log

should constitute a complete record of the passage.

Determining the tidal and current conditions of the port is crucial. This process is covered in depth in Chapter 35. In order to anticipate early or late transit, plot a graph of the tidal range for the 24-hour period centered on the scheduled time of arrival or departure. Depending on a vessel’s draft and the harbor’s depth, some vessels may be able to transit only at high tide. If this is this case, it is critically important to determine the time and range of the tide correctly.

The magnitude and direction of the current will give the navigator some idea of the set and drift the vessel will experience during the transit. This will allow him or her to plan in advance for any potential current effects in the vicinity of navigational hazards.

NOAA's National Ocean Services (NOS) ceased printing and distributing annual Tide Tables in 1995, however, Tide Tables are still printed and distributed under license through several commercial publishers. It is far more efficient to use a computer with appropriate software, or the internet, to compute tides and print out the graphs. These graphs can be posted on the bridge at the chart table for ready reference, and copies made for others involved in the piloting process. The NOAA Tide Prediction service can be accessed through the link provided in Figure 1104. Always remember actual conditions may be quite different from predicted data due to weather or other natural phenomena. In addition the Navigator should be aware of any changes in the draft readings caused by ballasting or the off/onload of material.

[Figure 1104 in Bowditch, Pub. No. 9: NOAA Tide Prediction Service. https://tidesandcurrents.noaa.gov/tide_predictions.html]

The navigator should obtain a weather report covering the route which s/he intends to transit. This will allow him or her to prepare for any adverse weather by stationing extra lookouts, adjusting speed for poor visibility, and preparing for radar navigation. If the weather is thick, consider standing off the harbor until it clears.

The navigator can receive weather information any number of ways. Military vessels may receive weather reports from their parent squadrons prior to coming into port. Marine band radio carries continuous weather reports. Many vessels are equipped with weather facsimile machines. Some navigators carry cellular phones to reach shoreside personnel and harbor control; these can also be

used to get weather reports from NOAA weather stations. If the ship is using a weather routing service for the voyage, it should provide forecasts when asked. Finally, if the vessel has an internet connection, this is an ideal source of weather data. NOAA weather data can be obtained via the link provided in Figure 1105. However they obtains the information, the navigator should have a good idea of the weather before entering piloting waters.

[Figure 1105 in Bowditch, Pub. No. 9: NOAA Weather Data. https://www.weather.gov/]

Assemble the entire navigation team for a piloting brief prior to entering or leaving port. The vessel’s captain and navigator should conduct the briefing. All navigation and bridge personnel should attend. The pilot, if s/he is already on board, should also attend. If the pilot is not onboard when the ship’s company is briefed, the navigator should immediately brief them when s/he embarks. The pilot must know the ship’s maneuvering characteristics before entering restricted waters. The briefing should cover, as a minimum, the following:

Detailed Coverage of the Track Plan: Go over the •

planned route in detail. Use the prepared and approved

chart as part of this brief. Concentrate especially on all

the NAVAIDS and soundings which are being used to

indicate danger. Cover the buoyage system in use and

the port’s major NAVAIDS. Point out the radar

NAVAIDS for the radar operator. Often, a Fleet Guide

or Sailing Directions will have pictures of a port’s

NAVAIDS. This is especially important for the pilot-

ing party that has never transited a particular port

before. If no pictures are available, consider stationing

a photographer to take some for submission to NGA.

Harbor Communications: Discuss the bridge-to •

bridge radio frequencies used to raise harbor control.

Discuss what channel the vessel is supposed to monitor

on its passage into port and the port’s communication

protocol.

Duties and Responsibilities: Each member of the •

piloting team must have a thorough understanding of

his or her duties and responsibilities. S/He must also

understand how his or her part fits into the whole. The

radar plotter, for example, must know if radar will be

the primary or secondary source of fix information.

The bearing recorder must know what fix interval the

navigator is planning to use. Each person must be thor-

oughly briefed on his or her job; there is little time for

questions once the vessel enters the channel.

The navigator should always accomplish the following evolutions prior to piloting:

Testing the Shaft on the Main Engines in the Astern •

Direction: This ensures that the ship can answer a

backing bell. If the ship is entering port, no special pre-

cautions are required prior to this test. If the ship is tied

up at the pier preparing to get underway, exercise

extreme caution to ensure no way is placed on the ship

while testing the main engines, and the area astern of

the vessel is clear of lines or other obstructions.

Making the Anchor Ready for Letting Go: Make the •

anchor ready for letting go and station a watchstander

in direct communications with the bridge at the anchor

windlass. Be prepared to drop anchor immediately

when piloting if required to keep from drifting too

close to a navigational hazard.

Calculate Gyro Error: An error of greater than 1.0° T •

indicates a gyro problem which should be investigated

prior to piloting. There are several ways to determine

gyro error:

1. Compare the gyro reading with a known accurate heading reference such as an inertial navigator. The difference in the readings is the gyro error.

2. Mark the bearing of a charted range as the range NAVAID’s come into line and compare the gyro bearing with the charted bearing. The difference is the gyro error. This is both the fastest and most accurate way to determine gyro error.

3. Prior to getting underway, plot a dockside fix using at least three lines of position. The three LOP’s should intersect at a point. Their intersecting in a “cocked hat” indicates a gyro error. Incrementally adjust each visual bearing by the same amount and direction until the fix plots as a pinpoint. The total correction required to eliminate the cocked hat is the gyro error.

4. Measure a celestial body’s azimuth or amplitude, or Polaris’ azimuth with the gyro, and then compare the measured value with a value computed from the Sight Reduction Tables or the Nautical Almanac. These methods are covered in detail in Chapter 15.

Report the magnitude and direction of the gyro error to

the navigator and captain. The direction of the error is determined by the relative magnitude of the gyro reading and the value against which it is compared. When the compass is least, the error is east. Conversely, when the compass is best, the error is west. See Chapter 8

The vessel’s planned estimated time of arrival (ETA) at its mooring determines the vessel’s course and speed to the harbor entrance. Arriving at the mooring site on time may be important in a busy port which operates its port services on a tight schedule. Therefore, it is important to plan the arrival accurately. Take the desired time of arrival at the mooring and subtract from that the time it will take to navigate to it from the entrance. The resulting time is when you must arrive at the harbor entrance. Next, measure the distance between the vessel’s present location and the harbor entrance. Determine the speed of advance (SOA) the vessel will use to make the transit to the harbor. Use the distance to the harbor and the SOA to calculate what time to leave the present position to make the mooring ETA, or what speed must be made good to arrive on time.

Consider these factors which might affect this decision:

Weather: This is the single most important factor in •

harbor approach planning because it directly affects the

vessel’s SOA. The thicker the weather, the more

slowly the vessel must proceed. Therefore, if heavy fog

or rain is in the forecast, the navigator must allow more

time for the transit.

Mooring Procedures: Navigators must take more •

than distance into account when calculating how long

it will take them to pilot to their mooring. If the vessel

needs a tug, that will increase the time needed. Simi-

larly, picking up or dropping off a pilot adds time to the

transit. It is better to allow a margin for error when try-

ing to add up all the time delays caused by these proce-

dures. It is always easier to avoid arriving early by

slowing down than it is to make up lost time by speed-

ing up.

Shipping Density: Generally, the higher the shipping •

density entering and exiting the harbor, the longer it

will take to proceed into the harbor entrance safely.

At the appropriate time, station the piloting team. Allow plenty of time to acclimate to the navigational situation and if at night, to the darkness. The number and type of personnel available for the piloting team depend on the vessel. A Navy warship, for example, has more people available for piloting than a merchant ship. Therefore, more than one of the jobs listed below may have to be filled by a single person. The piloting team should consist of:

The Captain: The captain is ultimately responsible for •

the safe navigation of the vessel. His or her judgment

regarding navigation is final. The piloting team acts to

support the captain, advising him or her so they can

make informed decisions on handling the vessel.

The Pilot: The pilot is usually the only member of the •

piloting team not a member of the ship’s company. The

piloting team must understand the relationship

between the pilot and the captain. The pilot is perhaps

the captain’s most important navigational advisor.

Generally, the captain will follow his or her recom-

mendations when navigating an unfamiliar harbor. The

pilot, too, bears some responsibility for the safe pas-

sage of the vessel; he or she can be censured for errors

of judgment which cause accidents. However, the pres-

ence of a pilot in no way relieves the captain of having

ultimate responsibility for safe navigation. One excep-

tion to this rule is in the Panama Canal per 32 CFR

700.857 where the Commanding Officer is relieved of

the responsibility for the safe navigation of the vessel

to the canal Pilot. The piloting team works to support

and advise the captain.

The Officer of the Deck (Conning Officer): In Navy •

piloting teams, neither the pilot or the captain usually

has the conn. The Officer of the Deck (OOD) and the

Conning Officer are two different watchstanders. The

OOD underway is in charge of the safe operation of the

ship and supervises the personnel on watch on the

bridge. The Conning Officer directs the ship’s move-

ments by rudder and engine orders. The captain can

take the conn immediately simply by issuing an order

to the helm should an emergency arise. The conning

officer of a merchant vessel can be either the pilot, the

captain, or another watch officer. In any event, the offi-

cer having the conn must be clearly indicated in the

ship’s deck log at all times. Often a single officer will

have the deck and the conn. However, sometimes a

junior officer will take the conn for training. In this

case, different officers will have the deck and the conn.

The officer who retains the deck retains the responsi-

bility for the vessel’s safe navigation. US Coast Guard

vessels normally split the deck and conn.

The Navigator: The vessel’s navigator is the officer •

directly responsible to the ship’s captain for the safe

navigation of the ship. S/He is the captain’s principal

navigational advisor. The piloting team works for the

captain. The navigator channels the required informa-

tion developed by the piloting team to the ship’s con-

ning officer on recommended courses, speeds, and

turns. The navigator also carefully looks ahead for

potential navigational hazards and makes appropriate

recommendations. S/He is the most senior officer who

devotes his or her effort exclusively to monitoring the

navigation picture. The captain and the conning officer

are concerned with all aspects of the passage, including

contact avoidance and other necessary ship evolutions

(making up tugs, maneuvering alongside a small boat

for personnel transfers, engineering evolutions, and

coordinating with harbor control via radio, for exam-

ple). The navigator, on the other hand, focuses solely

on safe navigation. It is his or her job to anticipate dan-

gers, keep themselves appraised of the navigation situ-

ation at all times, and manage the team.

Bearing Plotting Team: This team consists, ideally, •

of three persons. The first person measures the bear-

ings. The second person records the bearings in an offi-

cial record book. The third person plots the bearings.

The bearing taker should be an experienced individual

who has traversed the port before and who is familiar

with the NAVAIDS. He or she should take their round

of bearings as quickly as possible, beam bearings first,

minimizing any time delay errors in the resulting fix.

The plotter should also be an experienced individual

who can quickly and accurately lay down the required

bearings. The bearing recorder can be one of the junior

members of the piloting team.

The Radar Operator: The radar operator has one of •

the more difficult jobs of the team. The radar is as

important for collision avoidance as it is for navigation.

Therefore, this operator must often “time share” the

radar between these two functions. Determining the

amount of time spent on these functions falls within the

judgment of the captain and the navigator. If the day is

clear and the traffic heavy, the captain may want to use

the radar mostly for collision avoidance. As the

weather worsens, obscuring visual NAVAIDS, the

importance of radar for safe navigation increases. The

radar operator must be given clear guidance on how the

captain and navigator want the radar to be operated.

Plot Supervisors: On many military ships, the piloting •

team will consist of two plots: the primary plot and the

secondary plot. The navigator should designate the

type of navigation that will be employed on the pri-

mary plot. All other fix sources should be plotted on

the secondary plot. The navigator can function as the

primary plot supervisor. A senior, experienced individ-

ual should be employed as a secondary plot supervisor.

The navigator should frequently compare the positions

plotted on both plots as a check on the primary plot.

There are three major reasons for maintaining a

primary and secondary plot. First, as mentioned above,

the secondary fix sources provide a good check on the

accuracy of visual piloting. Large discrepancies

between visual and radar positions may point out a

problem with the visual fixes that the navigator might

not otherwise suspect. Secondly, the navigator often

must change the primary means of navigation during

the transit. S/He may initially designate visual bearings

as the primary fix method only to have a sudden storm

or fog obscure the visual NAVAIDS. If s/he shifts the

primary fix means to radar, s/he has a track history of

the correlation between radar and visual fixes. Finally,

the piloting team often must shift charts several times

during the transit. When the old chart is taken off the

plotting table and before the new chart is secured, there

is a period of time when no chart is in use. Maintaining

a secondary plot eliminates this complication. Ensure

the secondary plot is not shifted prior to getting the

new primary plot chart down on the chart table. In this

case, there will always be a chart available on which to

pilot. Do not consider the primary chart shifted until

the new chart is properly secured and the plotter has

transferred the last fix from the original chart onto the

new chart.

Fathometer Operator: Run the fathometer continu- •

ously and station an operator to monitor it. Do not rely

on audible alarms to key your attention to this critically

important piloting tool. The fathometer operator must

know the warning and danger soundings for the area

the vessel is transiting. Most fathometers can display

either total depth of water or depth under the keel. Set

the fathometer to display depth under the keel. The

navigator must check the sounding at each fix and

compare that value to the charted sounding. A discrep-

ancy between these values is cause for immediate

action to take another fix and check the ship’s position.

The piloting team must make the transition from coastal navigation to piloting smoothly as the vessel approaches restricted waters. There is no rigid demarcation between coastal navigation and piloting. Often visual NAVAIDS are visible miles from shore where GPS is easier to use. The navigator should take advantage of this overlap when approaching the harbor. Plotting GPS, and visual fixes concurrently ensures that the piloting team has correctly identified NAVAIDS and that the different types of systems are in agreement. Once the vessel is close enough to the shore such that sufficient NAVAIDS (at least three with sufficient bearing spread) become visible, the navigator should order visual bearings only for the primary plot and shift all other fixes to the secondary plot, unless the decision has been made to proceed with ECDIS as the primary system.

Take advantage of the coastal navigation and piloting overlap to shorten the fix interval gradually. The navigator must use his of her judgment in adjusting fix intervals. If the ship is steaming inbound directly towards the shore, set a

fix interval such that two fix intervals lie between the vessel and the nearest danger. Upon entering restricted waters, the piloting team should be plotting visual fixes at three minute intervals.

Commercial vessels with GPS, planning the harbor transit with a pilot, will approach a coast differently. The transition from ocean to coastal to harbor approach navigation will proceed as visual aids and radar targets appear and are plotted. Once the pilot is aboard, the captain/pilot team may elect to navigate visually, depending on the situation.

Safe navigation while piloting requires frequent fixing of the ship’s position whether the vessel is supported by ECDIS or not. If an ECS is in use, it should be considered only a supplement to the paper navigation plot, which legally must still be maintained. As long as the manual plot and the ECS plot are in agreement, the ECS is a valuable tool which shows the navigator where the ship is at any instant, not two or three minutes ago when the last fix was taken. It cannot legally take the place of the paper chart and the manual plot, but it can provide an additional measure of assurance that the ship is in safe water and alert the navigator to a developing dangerous situation before the next round of bearings or ranges.

The next several articles will discuss the three major manual methods used to fix a ship’s position when piloting: crossing lines of position, copying satellite data, or advancing a single line of position. Using one method does not exclude using other methods. The navigator must obtain as much information as possible and employ as many of these methods as necessary.

While the intersection of two LOP’s constitutes a fix under one definition, and only an estimated position by another, the prudent navigator will always use at least three LOP’s if they are available, so that an error is apparent if they don’t meet in a point. Some of the most commonly used methods of obtaining LOP’s are discussed below:

Fix by Bearings: The navigator can take and plot bear- •

ings from two or more charted objects. This is the most

common and often the most accurate way to fix a ves-

sel’s position. Bearings may be taken directly to

charted objects, or tangents of points of land. See Fig-

ure 1111a. The intersection of these lines constitutes a

fix. A position taken by bearings to buoys should not

be considered a fix, but an estimated position (EP),

because buoys swing about their watch circle and may

be out of position.

Fix by Ranges: The navigator can plot a fix consisting •

of the intersection of two or more range arcs from

charted objects. S/He can obtain an object’s range in

several ways:

1. Radar Ranges: See Figure 1111b. The navigator

may take ranges to two fixed objects. The intersec-

tion of the range arcs constitutes a fix. S/He can

[Figure 1111a in Bowditch, Pub. No. 9: A fix by two bearing lines.]

[Figure 1111b in Bowditch, Pub. No. 9: A fix by two radar ranges.]

plot ranges from any point on the radar scope which

s/he can correlate on his or her chart. Remember

that the shoreline of low-lying land may move

many yards in an area of large tidal range, and

swampy areas may be indistinct.

2. Stadimeter Ranges: Given a known height of a

[Figure 1111c in Bowditch, Pub. No. 9: Principle of stadimeter operation.]

NAVAID, one can use a stadimeter to determine its

range. See Figure 1111c for a representation of the

geometry involved. Generally, stadimeters contain

a height scale on which is set the height of the

object. The observer then directs his or her line of

sight through the stadimeter to the base of the

object being observed. Finally, s/he adjusts the sta-

dimeter’s range index until the object’s top reflec-

tion is “brought down” to the visible horizon. Read

the object’s range off the range index.

3. Sextant Vertical Angles: Measure the vertical

angle from the top of the NAVAID to the waterline

below the NAVAID. Enter Table 16 of Volume II

to determine the distance of the NAVAID. The

navigator must know the height of the NAVAID

above sea level to use this table; it can be found in

the Light List.

4. Sonar Ranges: If the vessel is equipped with a

sonar suite, the navigator can use sonar echoes to

determine ranges to charted underwater objects. It

may take some trial and error to set the active signal

strength at a value that will give a strong return and

still not cause excessive reverberation. Check local

harbor restrictions on energizing active sonar.

Avoid active sonar transmissions in the vicinity of

divers.

Fix by Bearing and Range: This is a hybrid fix of •

LOP’s from a bearing and range to a single object. The

radar is the only instrument that can give simultaneous

range and bearing information to the same object. (A

sonar system can also provide bearing and range infor-

mation, but sonar bearings are far too inaccurate to use

in piloting.) Therefore, with the radar, the navigator

can obtain an instantaneous fix from only one

NAVAID. This unique fix is shown in Figure 1111d.

This makes the radar an extremely useful tool for the

piloting team. The radar’s characteristics make it much

[Figure 1111d in Bowditch, Pub. No. 9: A fix by range and bearing of a single object.]

more accurate determining range than determining

bearing; therefore, two radar ranges are preferable to a

radar range and bearing.

Electronic Range Finder: A modern electronic range •

finder may be used for the same purpose as a stadime-

ter. The Coast Guard uses electronic range finders to

augment the stadimeter during underway replenish-

ment and other station keeping operations when ves-

sels are too close for accurate radar ranging.

Fix by Range Line and Distance: When the vessel •

comes in line with a range, plot the bearing to the range

(while checking compass error in the bargain) and

cross this LOP with a distance from another NAVAID.

Figure 1111e shows this fix.

When only one NAVAID is available from which to obtain bearings, use a technique known as the running fix. Use the following method: • Plot a bearing to a NAVAID (LOP 1).

[Figure 1111e in Bowditch, Pub. No. 9: A fix by a range and distance.]

• Plot a second bearing to a NAVAID (either the same

NAVAID or a different one) at a later time (LOP 2). • Advance LOP 1 to the time when LOP 2 was taken. • The intersection of LOP 2 and the advanced LOP 1

constitute the running fix.

Figure 1112a represents a ship proceeding on course 020°, speed 25 knots. At 1505, the plotter plots an LOP to a lighthouse bearing 310°. The ship can be at any point on this 1505 LOP. Some possible points are represented as points A, B, C, D, and E in Figure 1112a. Six minutes later the ship will have traveled 2.5 miles in direction 020°. If the ship was at A at 1505, it will be at A' at 1511. However, if the position at 1505 was B, the position at 1511 will be B'. A similar relationship exists between C and C', D and D', E and E'. Thus, if any point on the original LOP is moved a distance equal to the distance run in the direction of the motion, a line through this point parallel to the original line of position represents all possible positions of the ship at the later time. This process is called advancing a line of position. Moving a line back to an earlier time is called retiring a line of position.

When advancing a line of position, account for course changes, speed changes, and set and drift between the two bearing lines. Three methods of advancing an LOP are discussed below:

Method 1: See Figure 1112b. To advance the 1924 LOP to 1942, first apply the best estimate of set and drift to the 1942 DR position and label the resulting position point B. Then, measure the distance between the dead reckoning position at 1924 (point A) and point B. Advance the LOP a distance equal to the distance between points A and B. Note that LOP A'B' is in the same direction as line AB.

Method 2: See Figure 1112c. Advance the NAVAIDS position on the chart for the course and distance traveled by the vessel and draw the line of position from the NAVAIDS advanced position. This is the most satisfactory method for advancing a circle of position.

Method 3: See Figure 1112d. To advance the 1505 LOP to 1529, first draw a correction line from the 1505 DR position to the 1505 LOP. Next, apply a set and drift correction to the 1529 DR position. This results in a 1529 estimated position (EP). Then, draw from the 1529 EP a correc-

[Figure 1112a in Bowditch, Pub. No. 9: Advancing a line of position.]

[Figure 1112b in Bowditch, Pub. No. 9: Advancing a line of position with a change in course and speed, allowing for set and drift.]

[Figure 1112c in Bowditch, Pub. No. 9: Advancing a circle of position.]

tion line of the same length and direction as the one drawn from the 1505 DR to the 1505 LOP. Finally, parallel the 1505 bearing to the end of the correction line as shown.

Label an advanced line of position with both the time of observation and the time to which the line is adjusted.

Figure 1112e through Figure 1112g demonstrate three running fixes. Figure 1112e illustrates the case of obtaining a running fix with no change in course or speed between taking two bearings on the same NAVAID. Figure 1112f illustrates a running fix with changes in a vessel’s course and speed between taking two bearings on two different objects. Finally, Figure 1112g illustrates a running fix obtained by advancing range circles of position using the second method discussed above.

[Figure 1112d in Bowditch, Pub. No. 9: Advancing a line of position by its relation to the dead reckoning.]

[Figure 1112e in Bowditch, Pub. No. 9: A running fix by two bearings on the same object.]

The previous section discussed the methods for fixing the ship’s position. This section discusses integrating the manual fix methods discussed above, and the use of the fathometer, into a piloting procedure. The navigator must develop his or her piloting procedure to meet several requirements. He or she must obtain enough information to fix the position of the vessel without question. He or she must also plot and evaluate this information. Finally, s/he must relay his or her evaluation and recommendation to the vessel’s conning officer. This section examines some considerations to ensure the navigator accomplishes all these requirements quickly and effectively. Of course, if ECDIS is the primary plot, manual methods as discussed here are for backup use.

[Figure 1112f in Bowditch, Pub. No. 9: A running fix with a change of course and speed between observations on separate landmarks.]

[Figure 1112g in Bowditch, Pub. No. 9: A running fix by two circles of position.]

The preferred piloting fix is taken from visual bearings from charted fixed NAVAIDS. Plot visual bearings on the primary plot and plot all other fixes on the secondary plot. If poor visibility obscures visual NAVAIDS, shift to radar piloting on the primary plot. If neither visual nor radar piloting is available, consider standing off until the visibility improves.

The interval between fixes in restricted waters should usually not exceed three minutes. Setting the fix interval at three minutes optimizes the navigator’s ability to assimilate and evaluate all available information. He or she must relate it to charted navigational hazards and to his or her vessel’s intended track. It should take a well trained plotting team no more than 30 seconds to measure, record, and plot three bearings to three separate NAVAIDS. The navigator should spend the majority of the fix interval time interpreting the information, evaluating the navigational situation, and making recommendations to the conning officer.

If three minutes goes by without a fix, inform the captain and try to plot a fix as soon as possible. If the delay was caused by a loss of visibility, shift to radar piloting. If the delay was caused by plotting error, take another fix. If the navigator cannot get a fix down on the plot for several more minutes, consider slowing or stopping the ship until its position can be fixed. Never continue a passage through restricted waters if the vessel’s position is uncertain.

The secondary plot supervisor should maintain the same fix interval as the primary plot. Usually, this means s/he should plot a radar fix every three minutes. S/He should plot other fix sources (GPS fixes, for example) at an interval sufficient for making meaningful comparisons between fix sources. Every third fix interval, s/he should pass a radar fix to the primary plot for comparison with the visual fix. S/He should inform the navigator how well all the fix sources plotted on the secondary plot are tracking.

Following a cyclic routine ensures the timely and efficient processing of data and forms a smoothly functioning piloting team. It quickly gives the information which the navigator needs to make informed recommendations to the conning officer and captain.

Repeat this routine at each fix interval beginning when the ship gets underway until it clears the harbor (outbound) or when the ship enters the harbor until it is moored (inbound).

The routine consists of the following steps: • Take, plot and label a fix. • Calculate set and drift from the DR position. • Reset the DR from the fix and DR two fixes ahead.

Plotting the Fix: This involves coordination between •

the navigator, bearing taker(s), recorder, and plotter.

The navigator will call for each fix at the DR time. The

bearing taker must measure his or her bearings as

quickly as possible, beam bearings first, fore and aft

last, on the navigator’s mark. The recorder will write

the bearings in the book, and the plotter will plot them

immediately.

Labeling the Fix: The plotter should clearly mark a •

visual fix with a circle or an electronic fix with a trian-

gle. Clearly label the time of each fix. A visual running

fix should be circled, marked “R Fix” and labeled with

the time of the second LOP. Keep the chart neat and

uncluttered when labeling fixes.

Dead Reckoning Two Fix Intervals Ahead: After •

labeling the fix, the plotter should dead reckon the fix

position ahead two fix intervals. The navigator should

carefully check the area marked by this DR for any

navigational hazards. If the ship is approaching a turn,

update the turn bearing as discussed in Section 1102.

Calculate Set and Drift at Every Fix: Calculating set •

and drift is covered in Chapter 9. Calculate these val-

ues at every fix and inform the captain and conning

officer. Compare the actual values of set and drift with

the predicted values from the current graph discussed

in Section 1104. Evaluate how the current is affecting

the vessel’s position in relation to the track and recom-

mend courses and speeds to regain the planned track.

Because the navigator can determine set and drift only

when comparing fixes and DR’s plotted for the same

time, take fixes exactly at the times for which a DR has

been plotted. Repeat this routine at each fix interval

beginning when the ship gets underway until it clears

the harbor (outbound) or when the ship enters the har-

bor until she is moored (inbound).

Piloting Routine When Turning: Modify the cyclic •

routine slightly when approaching a turn. Adjust the fix

interval so that the plotting team has a fix plotted

approximately one minute before a scheduled turn.

This gives the navigator sufficient time to evaluate the

position in relation to the planned track, DR ahead to

the slide bar to determine a new turn bearing, relay the

new turn bearing to the conning officer, and then mon-

itor the turn bearing to mark the turn.

Approximately 30 seconds before the time to turn, train the alidade on the turn bearing NAVAID. Watch the bearing of the NAVAID approach the turn bearing. About 1° away from the turn bearing, announce to the conning officer: “Stand by to turn.” Slightly before the turn bearing is indicated, report to the conning officer: “Mark the turn.” Make this report slightly before the bearing is reached because it takes the conning officer a finite amount of time to acknowledge the report and order the helmsman to put over the rudder. Additionally, it takes a finite amount of

time for the helmsman to turn the rudder and for the ship to start to turn. If the navigator waits until the turn bearing is indicated to report the turn, the ship will turn too late.

Once the ship is steady on the new course, immediately take another fix to evaluate the vessel’s position in relation to the track. If the ship is not on the track after the turn, calculate and recommend a course to the conning officer to regain the track.

Use the fathometer to determine whether the depth of water under the keel is sufficient to prevent the ship from grounding and to check the actual water depth with the charted water depth at the fix position. The navigator must compare the charted sounding at every fix position with the fathometer reading and report to the captain any discrepancies. Taking continuous soundings in restricted waters is mandatory.

See the discussion of calculating the warning and danger soundings in Section 1102. If the warning sounding is received, then slow the ship, fix the ship’s position more frequently, and proceed with extreme caution. Ascertain immediately where the ship is in the channel; if the minimum expected sounding was noted correctly, the warning sounding indicates the vessel may be leaving the channel and standing into shoal water. Notify the vessel’s captain and conning officer immediately.

If the danger sounding is received, take immediate action to get the vessel back to deep water. Reverse the engines and stop the vessel’s forward movement. Turn in the direction of the deepest water before the vessel loses steerageway. Consider dropping the anchor to prevent the ship from drifting aground. The danger sounding indicates that the ship has left the channel and is standing into immediate danger. It requires immediate corrective action by the ship’s conning officer, navigator, and captain to avoid disaster.

Many underwater features are poorly surveyed. If a fathometer trace of a distinct underwater feature can be obtained along with accurate position information, send the fathometer trace and related navigational data to NGA for entry into the Digital Bathymetric Data Base.

Most U.S. Navy vessels receive instructions in their movement orders regarding the choice of anchorage. Merchant ships are often directed to specific anchorages by harbor authorities. However, lacking specific guidance, the mariner should choose his or her anchoring positions using the following criteria:

Depth of Water: Choose an area that will provide suf- •

ficient depth of water through an entire range of tides.

Water too shallow will cause the ship to go aground,

and water too deep will allow the anchor to drag.

Type of Bottom: Choose the bottom that will best hold •

the anchor. Avoid rocky bottoms and select sandy or

muddy bottoms if they are available.

Proximity to navigational Hazards: Choose an •

anchorage as far away as possible from known naviga-

tional hazards.

Proximity to Adjacent Ships: Anchor well away from •

adjacent vessels; ensure that another vessel will not

swing over your own anchor on a current or wind shift.

Proximity to Harbor Traffic Lanes: Anchor clear of •

traffic lanes and ensure that the vessel will not swing

into the channel on a current or wind shift.

Weather: Choose an area with the weakest winds and •

currents.

Availability of NAVAIDS: Choose an anchorage with •

several NAVAIDS available for monitoring the ship’s

position when anchored.

It is usually best to follow an established procedure to ensure an accurate positioning of the anchor, even when anchoring in an open roadstead. The following procedure is representative. See Figure 1117.

Locate the selected anchoring position on the chart. Consider limitations of land, current, shoals, and other vessels when determining the direction of approach. Where conditions permit, make the approach heading into the current. Close observation of any other anchored vessels will provide clues as to which way the ship will lie to her anchor. If wind and current are strong and from different directions, ships will lie to their anchors according to the balance between these two forces and the draft and trim of each ship. Different ships may lie at different headings in the same anchorage depending on the balance of forces affecting them.

Approach from a direction with a prominent NAVAID, preferably a range, available dead ahead to serve as a steering guide. If practicable, use a straight approach of at least 1200 yards to permit the vessel to steady on the required course. Draw in the approach track, allowing for advance and transfer during any turns. In Figure 1117, the chimney was selected as this steering bearing. A turn range may also be used if a radar-prominent object can be found directly ahead or astern.

Next, draw a circle with the selected position of the anchor as the center, and with a radius equal to the distance between the hawsepipe and pelorus, alidade, or periscope

[Figure 1117 in Bowditch, Pub. No. 9: Anchoring.]

used for measuring bearings. This circle is marked “A” in Figure 1117. The intersection of this circle and the approach track is the position of the vessel’s bearing-measuring instrument at the moment of letting the anchor go. Select a NAVAID which will be on the beam when the vessel is at the point of letting go the anchor. This NAVAID is marked “FS” in Figure 1117. Determine what the bearing to that object will be when the ship is at the drop point and measure this bearing to the nearest 0.1°T. Label this bearing as the letting go bearing.

During the approach to the anchorage, plot fixes at frequent intervals. The navigator must advise the conning officer of any tendency of the vessel to drift from the desired track. The navigator must frequently report to the conning officer the distance to go, permitting adjustment of the speed so that the vessel will be dead in the water or have very slight sternway when the anchor is let go. To aid in determining the distance to the drop point, draw and label a number of range arcs as shown in Figure 1117 representing distances to go to the drop point.

At the moment of letting the anchor go, take a fix and plot the vessel’s exact position on the chart. This is important in the construction of the swing and drag circles discussed below. To draw these circles accurately, determine the position of the vessel at the time of letting go the anchor as accurately as possible.

Veer the anchor chain to a length equal to five to seven times the depth of water at the anchorage. The exact amount to veer is a function of both vessel type and severity of weather expected at the anchorage. When calculating the scope of anchor chain to veer, take into account the maximum height of tide.

Once the ship is anchored, construct two separate circles around the ship’s position when the anchor was dropped. These circles are called the swing circle and the drag circle. Use the swing circle to check for navigational hazards and use the drag circle to ensure the anchor is holding.

The swing circle’s radius is equal to the sum of the ship’s length and the scope of the anchor chain released. This represents the maximum arc through which a ship can swing while riding at anchor if the anchor holds. Examine this swing circle carefully for navigational hazards, interfering contacts, and other anchored shipping. Use the lowest height of tide expected during the anchoring period when checking inside the swing circle for shoal water.

The drag circle’s radius equals the sum of the hawsepipe to pelorus distance and the scope of the chain

released. Any bearing taken to check on the position of the ship should, if the anchor is holding, fall within the drag circle. If a fix falls outside of that circle, then the anchor is dragging. If the vessel has a GPS or system with an off-station alarm, set the alarm at the drag circle radius, or slightly more.

In some cases, the difference between the radii of the swing and drag circles will be so small that, for a given chart scale, there will be no difference between the circles when plotted. If that is the case, plot only the swing circle and treat that circle as both a swing and a drag circle. On the other hand, if there is an appreciable difference in radii between the circles when plotted, plot both on the chart. Which method to use falls within the sound judgment of the navigator.

When determining if the anchor is holding or dragging, the most crucial period is immediately after anchoring. Fixes should be taken frequently, at least every three minutes, for the first thirty minutes after anchoring. The navigator should carefully evaluate each fix to determine if the anchor is holding. If the anchor is holding, the navigator can then increase the fix interval. What interval to set falls within the judgment of the navigator, but the interval should not exceed 30 minutes. If an ECDIS or GPS is available, use its off-station alarm feature for an additional safety factor.

A ship moving through shallow water experiences pronounced effects from the proximity of the nearby bottom. Similarly, a ship in a channel will be affected by the proximity of the sides of the channel. These effects can easily cause errors in piloting which lead to grounding. The effects are known as squat, bank cushion, and bank suction. They are more fully explained in texts on shiphandling, but certain navigational aspects are discussed below.

Squat is caused by the interaction of the hull of the ship, the bottom, and the water between. As a ship moves through shallow water, some of the water it displaces rushes under the vessel to rise again at the stern. This causes a venturi effect, decreasing upward pressure on the hull. Squat makes the ship sink deeper in the water than normal and slows the vessel. The faster the ship moves through shallow water, the greater is this effect; groundings on both charted and uncharted shoals and rocks have occurred because of this phenomenon, when at reduced speed the ship could have safely cleared the dangers. When navigating in shallow water, the navigator must reduce speed to avoid squat. If bow and stern waves nearly perpendicular the direction of travel are noticed, and the vessel slows with no change in shaft speed, squat is occurring. Immediately slow the ship to counter it. Squatting occurs in deep water also, but is more pronounced and dangerous in shoal water. The large waves generated by a squatting ship also endanger shore facilities and other craft.

Bank cushion is the effect on a ship approaching a steep underwater bank at an oblique angle. As water is forced into the narrowing gap between the ship’s bow and the shore, it tends to rise or pile up on the landward side, causing the ship to sheer away from the bank.

Bank suction occurs at the stern of a ship in a narrow channel. Water rushing past the ship on the landward side exerts less force than water on the opposite or open water side. This effect can actually be seen as a difference in draft readings from one side of the vessel to the other, and is similar to the venturi effect seen in squat. The stern of the ship is forced toward the bank. If the ship gets too close to the bank, it can be forced sideways into it. The same effect occurs between two vessels passing close to each other.

These effects increase as speed increases. Therefore, in shallow water and narrow channels, navigators should decrease speed to minimize these effects. Skilled pilots may use these effects to advantage in particular situations, but the average mariner’s best choice is slow speed and careful attention to piloting.

Current affects the accuracy of a running fix. Consider, for example, the situation of an unknown head current. In Figure 1119b, a ship is proceeding along a coast, on course 250 ° speed 12 knots. At 0920 light A bears 190°, and at 0930 it bears 143°. If the earlier bearing line is advanced a distance of 2 miles (10 minutes at 12 knots) in the direction of the course, the running fix is as shown by the solid lines. However, if there is a head current of 2 knots, the ship is making good a speed of only 10 knots, and in 10 minutes will travel a distance of only 1 2/3 miles. If the first bearing line is advanced this distance, as shown by the broken line, the actual position of the ship is at B. This actual position is nearer the shore than the running fix actually plotted. A following current, conversely, would show a position too far from the shore from which the bearing was measured.

If the navigator assumes a following current when advancing his or her LOP, the resulting running fix will plot further from the NAVAID than the vessel’s actual position. Conversely, if s/he assumes a head current, the running fix will plot closer to the NAVAID than the vessel’s actual

position. To ensure a margin of safety when plotting running fix bearings to a NAVAID on shore, always assume the current slows a vessel’s speed over ground. This will cause the running fix to plot closer to the shore than the ship’s actual position.

When taking the second running fix bearing from a different object, maximize the speed estimate if the second object is on the same side and farther forward, or on the opposite side and farther aft, than the first object was when observed.

All of these situations assume that danger is on the same side as the object observed first. If there is either a head or following current, a series of running fixes based upon a number of bearings of the same object will plot in a straight line parallel to the course line, as shown in Figure 1119a. The plotted line will be too close to the object observed if there is a head current and too far out if there is a following current. The existence of the current will not be apparent unless the actual speed over the ground is known. The position of the plotted line relative to the dead reckoning course line is not a reliable guide.

[Figure 1119a in Bowditch, Pub. No. 9: A number of running fixes with a following current.]

A current oblique to a vessel’s course will also result in an incorrect running fix position. An oblique current can be detected by observing and plotting several bearings of the same object. The running fix obtained by advancing one bearing line to the time of the next one will not agree with the running fix obtained by advancing an earlier line. See Figure 1120a. If bearings A, B, and C are observed at five-minute intervals, the running fix obtained by advancing B to the time of C will not be the same as that obtained by advancing A to the time of C, as shown in Figure 1120a.

[Figure 1119b in Bowditch, Pub. No. 9: Effect of a head current on a running fix.]

[Figure 1120a in Bowditch, Pub. No. 9: Detecting the existence of an oblique current, by a series of running fixes.]

Whatever the current, the navigator can determine the direction of the track made good (assuming constant current and constant course and speed). Observe and plot three bearings of a charted object O. See Figure 1120b. Through O draw XY in any direction. Using a convenient scale, determine points A and B so that OA and OB are proportional to the time intervals between the first and second

[Figure 1120b in Bowditch, Pub. No. 9: Determining the track made good.]

bearings and the second and third bearings, respectively. From A and B draw lines parallel to the second bearing line, intersecting the first and third bearing lines at C and D, respectively. The direction of the line from C and D is the track made good.

The distance of the line CD in Figure 1120b from the track is in error by an amount proportional to the ratio of the speed made good to the speed assumed for the solution. If a good fix (not a running fix) is obtained at some time before the first bearing for the running fix, and the current has not changed, the track can be determined by drawing a line from the fix, in the direction of the track made good. The intersection of the track with any of the bearing lines is an actual position.

Geometrical relationships can define a running fix. In Figure 1121, the navigator takes a bearing on NAVAID D. The bearing is expressed as degrees right or left of course. Later, at B, s/he takes a second bearing to D; similarly, s/he takes a bearing at C, when the landmark is broad on the beam. The navigator knows the angles at A, B, and C and the distance run between points. The various triangles can be solved using Table 18. From this table, the navigator can calculate the lengths of segments AD, BD, and CD. S/He knows the range and bearing; s/he can then plot an LOP. S/He can then advance these LOP’s to the time of taking the CD bearing to plot a running fix.

Enter the table with the difference between the course and first bearing (angle BAD in Figure 1121) along the top of the table and the difference between the course and second bearing (angle CBD) at the left of the table. For each pair of angles listed, two numbers are given. To find the distance from the landmark at the time of the second bearing (BD), multiply the distance run between bearings (in nautical miles) by the first number from Table 18. To find the distance when the object is abeam (CD), multiply the distance run between A and B by the second number from the table. If the run between bearings is exactly 1 mile, the tabulated values are the distances sought. Example: A ship is steaming on course 050°, speed 15 knots. At 1130 a lighthouse bears 024°, and at 1140 it bears 359°. Required:

[Figure 1121 in Bowditch, Pub. No. 9: Triangles involved in a Table 18 running fix.]

Distance from the light at 1140. •

Distance from the light when it is broad on the port •

beam. Solution:

The difference between the course and the first bearing •

(050° – 24°) is 26°, and the difference between the

course and the second bearing (050° + 360° - 359°) is

51°.

From Table 18 of Volume II, the two numbers (factors •

are 1.04 and 0.81, found by interpolation.

The distance run between bearings is 2.5 miles (10 •

minutes at 15 knots).

The distance from the lighthouse at the time of the sec- •

ond bearing is 2.5 × 1.04 = 2.6 miles.

The distance from the lighthouse when it is broad on •

the beam is 2.5 × 0.81 = 2.0 miles. Answers: (1) D 2.6 mi., (2) D 2.0 mi.

This method yields accurate results only if the helmsman has steered a steady course and the navigator uses the vessel’s speed over ground.

Piloting requires a thorough familiarity with principles involved, constant alertness, and judgment. A study of groundings reveals that the cause of most is a failure to use or interpret available information. Among the more common errors are: • Failure to obtain or evaluate soundings • Misidentification of aids to navigation • Failure to use available navigational aids effectively • Failure to correct charts • Failure to adjust a magnetic compass or keep a table of

corrections • Failure to apply deviation • Failure to apply variation • Failure to check gyro and magnetic compass readings

regularly • Failure to keep a dead reckoning plot • Failure to plot new information • Failure to properly evaluate information • Poor judgment • Failure to use information in charts and navigational

publications • Poor navigation team organization • Failure to “keep ahead of the vessel” • Failure to have backup navigational methods in place • Failure to recognize degradation of electronically

obtained LOP’s or lat./long. positions • Failure to slow down when in doubt of ship’s location

Some of the errors listed above are mechanical and some are matters of judgment. Conscientiously applying the principles and procedures of this chapter will go a long way towards eliminating many of the mechanical errors. However, the navigator must guard against the feeling that in following a checklist s/he has eliminated all sources of error. A navigator’s judgment is just as important as his or her checklists.

When measuring bearings from two NAVAIDS, the fix error resulting from an error held constant for both observations is minimized if the angle of intersection of the bearings is 90°. If the observer in Figure 1123a is located at point T and the bearings of a beacon and cupola are observed and plotted without error, the intersection of the bearing lines lies on the circumference of a circle passing through the beacon, cupola, and the observer. With constant error, the angular difference between the bearings of the beacon and the cupola is not affected. Thus, the angle formed at point F by the bearing lines plotted with constant error is equal to the angle formed at point T by the bearing lines plotted without error. From geometry it is known that angles having their apexes on the circumference of a circle and that are subtended by the same chord are equal. Since the angles at points T and F are equal and the angles are subtended by the same chord, the intersection at point F lies on the circumference of a circle passing through the beacon, cupola, and the observer.

[Figure 1123a in Bowditch, Pub. No. 9: Two-bearing plot.]

[Figure 1123b in Bowditch, Pub. No. 9: Two-bearing plot with constant error.]

Assuming only constant error in the plot, the direction of displacement of the two-bearing fix from the position of the observer is in accordance with the sign (or direction) of the constant error. However, a third bearing is required to determine the direction of the constant error.

Assuming only constant error in the plot, the two-bearing fix lies on the circumference of the circle pass-

ing through the two charted objects observed and the observer. The fix error, the length of the chord FT in Figure 1123b, depends on the magnitude of the constant error ∈, the distance between the charted objects, and the cosecant of the angle of cut, angle θ. In Figure 1123b, BC csc θ The fix error FT = = ------------------- where ∈ is the magnitude of the constant error, BC is the length of the chord BC, and θ is the angle of the LOP’s intersection.

Since the fix error is a function of the cosecant of the angle of intersection, it is least when the angle of intersection is 90°. As illustrated in Figure 1123c, the error increases in accordance with the cosecant function as the angle of intersection decreases. The increase in the error becomes quite rapid after the angle of intersection has decreased to below about 30°. With an angle of intersection of 30°, the fix error is about twice that at 90°.

If several fixes obtained by bearings on three objects produce triangles of error of about the same size, there might be a constant error in observing or plotting the bearings. If applying of a constant error to all bearings results in a pinpoint fix, apply such a correction to all subsequent fixes. Figure 1124a illustrates this technique. The solid lines indicate the original plot, and the broken lines indicate each line of position moved 3° in a clockwise direction.

[Figure 1123c in Bowditch, Pub. No. 9: Error of two-bearing plot.]

Employ this procedure carefully. Attempt to find and eliminate the error source. The error may be in the gyrocompass, the repeater, or the bearing transmission system. Compare the resulting fix positions with a satellite position, a radar position, or the charted sounding. A high degree of correlation between these three independent positioning systems and an “adjusted” visual fix is further confirmation of a constant bearing error.

Civilian piloting training has traditionally been a function of both maritime academies and on-the-job experience. The latter is usually more valuable, because there is no substitute for experience in developing judgment. In addition to at-sea training, the US Navy trains Surface Warfare Officers in Navigation and Shiphandling utilizing Conning Officer Virtual Environment (COVE) simulators. Junior Officers to Senior Commanding officers use these frequently throughout their careers to improve their skills and train on the various types of vessels they may serve on. Military vessels in general have a much clearer definition of responsibilities, as well as more people to carry them out, than civilian ships, so training is generally more thorough and targeted to specific skills.

Computer technology has made possible the development of computerized ship simulators by the US Navy and Coast Guard, which allow piloting experience to be gained without risking accidents at sea and without incurring underway expenses. Simulators enable shipboard navigation teams to train and complete required navigation drills. Simulators range from simple micro-computer-based software to a completely equipped ship’s bridge with radar, engine controls, 360° horizon views, programmable sea motions, and the capability to simulate almost any navigational situation. See Figure 1125b.

A different type of simulator consists of scale models of ships. The models, actually small craft of about 20-30 feet, have hull forms and power-to-weight ratios similar to various types of ships, primarily supertankers, and the operator pilots the vessel from a position such that his or her view is from the craft’s “bridge.” These are primarily used in training pilots and masters in docking maneuvers with exceptionally large vessels. For more about scale model shiphandling see Figure 1125a for a link to Port Revel.

The first computer ship simulators came into use in the late 1970s. Several years later the U.S. Coast Guard began accepting a limited amount of simulator time as “sea time” for licensing purposes. They can simulate virtually any conditions encountered at sea or in piloting waters, including land, aids to navigation, ice, wind, fog, snow, rain, and

[Figure 1124a in Bowditch, Pub. No. 9: Adjusting a fix for constant error.]

[Figure 1125a in Bowditch, Pub. No. 9: Port Revel. https://www.portrevel.com/]

lightning. The system can also be programmed to simulate hydrodynamic effects such as shallow water, passing vessels, current, and tugs.

Virtually any type of vessel can be simulated, including tankers, bulkers, container ships, tugs and barges, yachts, and military vessels. Similarly, any given navigational situation can be modeled, including passage through any chosen harbor, river, or passage, convoy operations, meeting and passing situations at sea and in harbors.

Simulators are used not only to train mariners, but also to test feasibility of port and harbor plans and visual aids to navigation system designs. This allows pilots to “navigate” simulated ships through simulated harbors before construction begins to test the adequacy of channels, turning basins, aids to navigation, and other factors.

A full-capability simulator consists of a ship’s bridge which may have motion and noise/vibration inputs, a programmable visual display system which projects a simulated picture of the area surrounding the vessel in both daylight and night modes, image generators for the various inputs to the scenario such as video images and radar, a central data processor, a human factors monitoring system which may record and videotape bridge activities for later analysis, and a control station where instructors control the entire scenario.

Some simulators are part-task in nature, providing specific training in only one aspect of navigation such as radar navigation, collision avoidance, or night navigation.

While there is no substitute for on-the-job training, simulators are extremely cost effective systems which can be run for a fraction of the cost of an actual vessel. Further, they permit trainees to learn from mistakes with no possibility of an accident, they can model an infinite variety of scenarios, and they permit replay and reassessment of each maneuver.

[Figure 1125b in Bowditch, Pub. No. 9: Navigational bridge simulator.]

The marine sextant has long been an accurate means for fixing a vessel’s position in coastal and confined water circumstances. However, with the advent of reliable gyrocompass technologies, followed by the introduction of precise electronic positioning systems like GPS, use of the marine sextant for terrestrial navigation has declined to such an extent that it is seldom employed during normal piloting conditions. This is unfortunate because the sextant can be used to great advantage in situations where other methods or tools, including the gyrocompass, are inadequate. The applications of the sextant during daylight in coastal waters, harbor approaches, and more confined waters may be summarized as follows:

1. fixing to make a safe transit of hazardous waters;

2. fixing to take a specific geographic position;

3. fixing to establish accurately the position of the anchor on anchoring;

4. fixing to determine whether or not the ship is dragging anchor;

5. using horizontal and vertical danger angles;

6. using vertical angles to determine distance off;

7. fixing to determine the positions of uncharted objects, or to verify the positions of charted features;

8. using the sextant to validate the accuracy of navigation by other means.

Because the use of the sextant has declined, many navigators, unfortunately, do not have the proficiency necessary to use it to advantage in those situations where other methods may be inadequate. Proficiency in the use of the sextant can be invaluable in situations where even a small error in either observing or plotting cross bearings could result in navigation blunder.

Normally, three charted objects are selected for measuring horizontal sextant angles to determine the observer's position, one of the objects being common to each angular measurement. With simultaneous or nearly simultaneous measurements of the horizontal angles between each pair of charted objects, the observer establishes two circles of position. For each pair of objects, there is only one circle which passes through the two objects and the observer's position. Thus, there are two circles, intersecting at two points as shown in Figure 1201a, which pass through the observer's position at T.

[Figure 1201a in Bowditch, Pub. No. 9: Solving the three-point problem.]

Since the observer knows that s/he is not at the intersection at B, s/he must be at T.

The solution of what is known as the three-point problem is effected by placing the hairlines of the arms of a plastic three-arm protractor over the three observed objects on the chart as shown in Figure 1201a. With the arms so placed, the center of the protractor disk is over the observer's position on the chart at the time of the measurements.

Although the conventional solution of the three-point problem is obtained by placing the arms of a three-arm protractor over the three observed objects on the chart, the use of the protractor is not necessary. The use of the protractor may not be practicable because of limited space and facilities for plotting, as in a small open boat. Where a common charted object cannot be used in the horizontal angle observations, a means other than the three-arm protractor must be employed to determine the position of the observer. Also, point fixes as obtained from the three-arm protractor can be

[Figure 1201b in Bowditch, Pub. No. 9: Use of the three-armed protractor.]

misleading if the navigator has limited skill in evaluating the strengths of the three-point solutions.

In plotting the three-point fix without a three-arm protractor, the procedure is to find the center of each circle of position, sometimes called circle of equal angle (Figure 1202a), and then, about such center, to strike an arc of radius equal to the distance on the chart from the circle center to one of the two objects through which the circle passes. The same procedure is applied to the other pair of objects to establish the fix at the intersection of the two arcs.

Some of the methods for finding the center of a circle of equal angle are described in the following text.

The center of the circle of equal angle lies on the perpendicular bisector of the baseline of the pair of objects. With the bisector properly graduated (Figure 1202b), one need only to place one point of the compasses at the appropriate graduation, the other point at one of the observed objects, and then to strike the circle of equal angle or an arc of it in the vicinity of the DR.

The bisector can be graduated through calculation or by means of either the simple protractor or the three-arm protractor.

As shown in Figure 1202a, when the observed angle is 90°, the center of the circle of equal angle lies at the center of the baseline or at the foot of the perpendicular bisector of the baseline. When the observed angle is less than 90°, for example 40°, the center of the circle lies on the perpendicular bisector on the same side of the baseline as the observer. When the observed angle is 26°34 ', the center of the circle lies on the bisector at a distance from its foot equal to the distance between the two objects. When the observed angle is greater than 90°, the center of the circle lies on the perpendicular bisector on the side of the baseline opposite from the observer. The center for 100° is the same distance from the baseline as the center for 80°; the center for 110° is the same distance as the center for 70°, etc. These facts can be used to construct a nomogram for finding the distances of circles of equal angle from the foot of the perpendicular for various angles.

[Figure 1202a in Bowditch, Pub. No. 9: Circles of equal angle.]

[Figure 1202b in Bowditch, Pub. No. 9: Graduated perpendicular bisector.]

From geometry the central angle subtended by a chord is twice the angle with its vertex on the circle and subtended by the same chord. Therefore, when the observed horizontal

angle is 30°, the central angle subtended by the baseline is 60°. Or, the angle at the center of the circle between the perpendicular bisector and the line in the direction of one of the observed objects is equal to the observed angle, or 30° as shown in Figure 1202c. The angle at the object between the baseline and the center of the circle on the bisector is 90° minus observed angle, or 60°.

[Figure 1202c in Bowditch, Pub. No. 9: Circle of equal angle (30°).]

Occasions when a common charted object cannot be used in horizontal angle observations are rare. On these occasions the mariner must obtain what is called a split fix through observation of two pairs of charted objects, with no object being common. As with the three-point fix, the mariner will obtain two circles of equal angle, intersecting at two points. As shown in Figure 1203, one of these two intersections will fix the observer's position.

[Figure 1203 in Bowditch, Pub. No. 9: Split fix.]

Preconstructed circles of equal angle can be helpful in conning the vessel to a specific geographic position when fixing by horizontal angles. In one application, the vessel is conned to keep one angle constant, or nearly constant, in order to follow the circumference of the associated circle of equal angle to the desired position; the other angle is changing rapidly and is approaching the value for the second circle of equal angle passing through the desired position.

Although an experienced navigator can readily estimate the strength of a three-point fix, and is able to select the objects providing the strongest fix available quickly, others often have difficulty in visualizing the problem and may select a weak fix when strong ones are available. The following generally useful (but not infallible) rules apply to selection of charted objects to be observed:

1. The strongest fix is obtained when the observer is inside the triangle formed by the three objects. And in such case the fix is strongest where the three objects form an equilateral triangle (Figure 1205, view A), the observer is at the center, and the objects are close to the observer.

2. The fix is strong when the sum of the two angles is equal to or greater than 180 ° and neither angle is less than 30°. The nearer the angles are equal to each other, the stronger is the fix (view B).

3. The fix is strong when the three objects lie in a straight line and the center object is nearest the observer (view C).

4. The fix is strong when the center object lies between the observer and a line joining the other two, and the center object is nearest the observer (view D).

5. The fix is strong when two objects a considerable distance apart are in range and the angle to the third object is greater than 45 ° (view E).

6. Small angles should be avoided as they result in weak fixes in most cases and are difficult to plot. However, a strong fix is obtained when two objects are nearly in range and the nearest one is used as the common object. The small angle must be measured very accurately, and the position of the two objects in range must be very accurately plotted. Otherwise, large errors in position will result. Such fixes are strong only when the common object is nearest the observer. The fix will become very weak where the observer moves to a position where the distant object is the common object (view F).

7. A fix is strong when at least one of the angles changes rapidly as the vessel moves from one location to another.

8. The sum of the two angles should not be less than 50°; better results are obtained when neither angle is less than 30 °.

9. Do not observe an angle between objects of considerably different elevation. Indefinite objects such as tangents, hill-tops, and other poorly defined or located points should not be used. Take care to select prominent objects

[Figure 1205 in Bowditch, Pub. No. 9: Strengths of three-point fixes.]

such as major lights, church spires, towers or buildings which are charted and are readily distinguished from surrounding objects.

Beginners should demonstrate the validity of the above rules by plotting examples of each and their opposites. It should be noted that a fix is strong if, in plotting, a slight movement of the center of the protractor moves the arms away from one or more of the stations, and is weak if such movement does not appreciably change the relation of the arms to the three points. An appreciation of the accuracy required in measuring angles can be obtained by changing one angle about five minutes in arc in each example and noting the resulting shift in the plotted positions;

The error of the three-point fix will be due to:

1. error in measurement of the horizontal angles;

2. error resulting from observer and observed objects not lying in a horizontal plane;

3. instrument error; and

4. plotting error.

The magnitude of the error varies directly as the error in measurement, the distance of the common object from

the observer, (D) and inversely as the sine function of the angle of cut (θ). The magnitude of the error also depends upon the following ratios:

1. The distance to the object to the left of the observer divided by the distance from this object to the center object (r1).

2. The distance to the object to the right of the observer divided by the distance from this object to the center object (r2).

Assuming that each horizontal angle has the same error

), the magnitude of the error (E) is expressed in the for- ( α mula

where error in measurement ( ) is expressed in radians.

The magnitude of the error (E) is expressed in the formula where error in measurement ( ) is expressed in minutes of arc.

To avoid mistakes in the identification of charted objects observed, either a check bearing or a check angle should be used to insure that the objects used in observation and plotting are the same.

Avoid a selection of objects which will result in a “revolver” or “swinger”; that is, when the three objects observed on shore and the ship are all on, or near, the circumference of a circle (Figure 1206). In such a case the ship's position is indeterminate by three-point fix.

[Figure 1206 in Bowditch, Pub. No. 9: Revolver or swinger.]

If bearings as plotted are affected by unknown and uncorrected compass error, the bearing lines may intersect at a point when the objects observed ashore and the ship are all on, or near, the circumference of a circle.

To cut in or locate on the chart uncharted objects, such as newly discovered offshore wrecks or objects ashore which may be useful for future observations, proceed as follows:

1. Fix successive positions of the ship or ship's boat by three-point fixes, i.e., by horizontal sextant angles. At each fix, simultaneously measure the sextant angle between one of the objects used in the fix and the object to be charted (Figure 1207a). For more accurate results, the craft from which the observations are made should be either lying to or proceeding slowly.

2. For best results, the angles should be measured simultaneously. If verification is undertaken, the angles observed should be interchanged among observers.

3. The fix positions should be selected carefully to give strong fixes, and so that the cuts to the object will provide a good intersection at the next station taken for observations. A minimum of three cuts should be taken.

An alternative procedure is to select observing positions so that the object to be charted will be in range with one of the charted objects used to obtain the three-point fix (Figure 1207b). The charted objects should be selected to provide the best possible intersections at the position of the uncharted object.

[Figure 1207a in Bowditch, Pub. No. 9: Cutting in uncharted objects.]

A vessel proceeding along a coast may be in safe water as long as it remains a minimum distance off the beach. This information may be provided by any means available. One method useful in avoiding particular dangers is the use of a danger angle. Refer to Figure 1208. A ship is proceeding along a coast on course line AB, and the captain wishes to remain outside a danger D. Prominent landmarks are lo-

[Figure 1207b in Bowditch, Pub. No. 9: On range method.]

cated at M and N. A circle is drawn through M and N and tangent to the outer edge of the danger. If X is a point on this circle, angle MXN is the same as at any other point on the circle (except that part between M and N). Anywhere within the circle the angle is larger and anywhere outside the circle it is smaller. Therefore, any angle smaller than MXN indicates a safe position and any angle larger than MXN indicates possible danger. Angle MXN is therefore a maximum horizontal danger angle. A minimum horizontal danger angle is used when a vessel is to pass inside an off-lying danger, as at D' in Figure 1108. In this case the circle is drawn through M and N and tangent to the inner edge of the danger area. The angle is kept larger than MYN. If a vessel is to pass between two danger areas, as in Figure 1208, the horizontal angle should be kept smaller than MXN but larger than MYN. The minimum danger angle is effective only while the vessel is inside the larger circle through M and N. Bearings on either landmark might be used to indicate the entering and leaving of the larger circle. A margin of safety can be provided by drawing the circles through points a short distance off the dangers. Any method of measuring the angles, or difference of bearing of M and N, can be used. Perhaps the most accurate is by horizontal sextant angle. If a single landmark of known height is available, similar procedure can be used with a vertical danger angle between top and bottom of the object. In this case the charted position of the object is used as the center of the circles.

[Figure 1208 in Bowditch, Pub. No. 9: Horizontal danger angles.]

Table 16 (Distance by Vertical Angle) provides means for determining the distance of an object of known height above sea level. The vertical sextant angle between the top of the object and the visible (sea) horizon is measured and corrected for index error and dip only. If a lighthouse is used for vertical sextant angle, the center of the lantern must be use, instead of the physical top of the lighthouse (Figure 1209). If the visible horizon is not available as a reference, the angle should be measured to the bottom of the object, and dip short of the horizon (Table 14) used in place of the usual dip correction. This may require several approximations of distance by alternate entries of Tables 16 and 15 until the same value is obtained twice. The table is entered with the difference in the height of the object and the height of eye of the observer, in feet, and the corrected vertical angle; and the distance in nautical miles is taken directly from the table. An error may be introduced if refraction differs from the standard value used in the computation of the table. See the Explanation of Tables section in Volume II for more details.

[Figure 1209 in Bowditch, Pub. No. 9: Vertical angle between the top of an object and the waterline, not vertically below the top of the object.]

As time and conditions permit, it behooves the navigator to use the sextant to evaluate the accuracy of navigation by other means in pilot waters. Such accuracy comparisons tend to provide navigators with better appreciation of the limitations of fixing by various methods in a given piloting situation.

The question (Q171 #40). You are steering 173°T, and a light is picked up dead ahead at a distance of 13.9 miles at 0054. You change course to pass the light 4.5 miles off abeam to port. If you are making 21 knots, what is your ETA at the position 4.5 miles off the light?

The working.

1. The light is DEAD AHEAD at 13.9 miles, and you are going to alter course so that it passes 4.5 miles off. Those two distances are two sides of a right-angled triangle: the 13.9 is the hypotenuse, and the 4.5 is the side opposite your position.
2. The distance you must run before it is abeam is the third side: √(13.9² − 4.5²) = √(193.21 − 20.25) = √172.96 = 13.2 miles.
3. Time = distance ÷ speed: 13.2 ÷ 21 = 0.626 hours.
4. 0.626 × 60 = 37.6 minutes.
5. 0054 + 37.6 minutes = 0131. A clock reads 0131 until 0132, so that is the whole minute you arrive in.

Answer: 0131.

What the paper is testing. Dividing the sighted range of 13.9 by 21 gives 39.7 minutes and an ETA of 0134 — which is on the paper. You do not run 13.9 miles: the moment the light is abeam you are still 4.5 miles from it, and that leg is the one you subtract.

The question (Q171 #41). While on a course of 321°T, a light bears 7° on the starboard bow at a distance of 9.7 miles. What course should you steer to pass 3.5 miles abeam of the light leaving it to starboard?

The working.

1. First put the light somewhere. It bears 7° on the STARBOARD bow of a course of 321°T, so its true bearing is 321 + 7 = 328°T, at 9.7 miles.
2. Now forget your present course: the question is what line through your position passes 3.5 miles from a point 9.7 miles away on 328°T.
3. That line makes an angle with the bearing of the light whose sine is 3.5 ÷ 9.7 = 0.361 — so the angle is 21°.
4. Which side to open it depends on where you want the light. To leave it to STARBOARD, steer to the left of it: 328 − 21 = 307°T.
5. Check it: the light then bears 21° on your starboard bow at 9.7 miles, and 9.7 × sin 21° = 3.5 miles when it comes abeam.

Answer: 307°T.

What the paper is testing. Opening the angle from your present course instead of from the bearing of the light gives 321 − 21 = 300°T, which is on the paper. The 7° is not part of the answer; it is only how you find where the light is.

The question (Q171 #44). You are underway on course 215°T at 12 knots. The current is 000°T at 2.3 knots. What is the course made good?

The working.

1. This is the vector diagram of § 1008, done with numbers instead of dividers. Draw the vessel's course and speed, then from the end of it the current's set and drift; the line closing the triangle is the course and speed made good.
2. A current 'at 000°T' SETS toward 000 — the opposite convention to a wind, which is named for where it comes from.
3. Break each into north–south and east–west. Vessel: 12 knots on 215°T is 12 × sin 215 = 6.9 knots WEST and 12 × cos 215 = 9.8 knots SOUTH. Current: 2.3 knots NORTH, nothing east or west.
4. Add them: 6.9 west stands, and 9.8 south − 2.3 north = 7.5 south.
5. The resultant: direction = 180 + arctan(6.9 ÷ 7.5) = 222°T. Speed made good = √(6.9² + 7.5²) = 10.2 knots.

Answer: 222°T.

What the paper is testing. The current has no easting or westing, so it cannot push you east or west — it can only cut your southing, which swings the track clockwise from 215 to 222 and costs you nearly two knots. The paper offers 209°T, which is this same triangle closed the wrong way round. Sketch it before you trust the arithmetic: a northerly current on a southwesterly course must open the course toward the west.