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Chapter 6

Dead Reckoning and Piloting Techniques

Navigation is defined as the art and science of safely directing the movement of a vessel from one position to another. Navigation is divided into four subdivisions: dead reckoning; piloting; celestial; and electronic. This chapter only covers dead reckoning and piloting navigation (along with their instruments and navigation aids).


  6-1. The magnetic compass is one of the oldest items of navigational equipment. It gets its source of power from the earth's magnetic field. Despite the rising importance and great convenience of the gyrocompass, the magnetic compass still retains its importance because of its simplicity and reliability. The magnetic compass will remain operative even when a ship is subjected to the following:
  • Electrical power failure.
  • Fire.
  • Collision.
  • Grounding.
  • Other hazards.
  6-2. To fully understand the operation of the magnetic compass, it is necessary to know something about magnets themselves. A magnet is a body that has the property of attracting iron and producing a magnetic field around itself.
  6-3. Magnetism that is present only when the material is under the influence of an external field is called "induced magnetism." Residual magnetism is the magnetism remaining after the magnetizing force is removed. Permanent magnetism is the magnetism remaining for long periods without appreciable reduction unless the material is subjected to a demagnetizing force. Such materials are lodestone and magnetic oxide of iron, which in their natural state possess this property. The earth itself has similar properties and may be considered a gigantic magnet.
  6-4. Every magnet has a north pole and a south pole. If a single magnet is cut in half, each half becomes a magnet with a north pole and a south pole. If two magnets are brought close together, their unlike poles will attract and their like poles repel. Therefore, a north pole attracts a south pole but repels another north pole. This law of magnetism has meaning as you learn how the magnets in a ship's magnetic compass conform to this law in relation to the earth's magnetic field or to the ship's own magnetic properties.
  6-5. The earth, like all other magnets, has a magnetic north pole and magnetic south pole. The magnetic north pole is located at an approximate latitude and longitude of 74° N and 101° W. The magnetic south pole is located at an approximate latitude and longitude of 68° S and 144° E. These magnetic poles are distinguished from the true North Pole, latitude of 90° N and the true South Pole, latitude of 90° S (see Figure 6-1).
  6-6. The magnetic lines of force that connect the magnetic poles are called "magnetic meridians." These meridians are not great circles. Because of the irregular distribution of magnetic material in the earth, the meridians are irregular, and the planes of the magnetic meridians do not pass through the center of the earth. Approximately midway between the magnetic poles is a line called the "magnetic equator." The magnetic equator is an irregular arc, varying in latitude from 15° S in South America to 20° S in Africa.
  6-7. Colors have been assigned to avoid confusion when speaking of the action of poles. The earth's north magnetic pole is designated as "blue" and the south magnetic pole is designated as "red." A law of magnetism states that "unlike poles" attract each other while "like poles" repel. Therefore, the north-seeking pole of a magnet is attracted to the earth's north magnetic pole and is "red" while the south-seeking pole is attracted by the earth's south magnetic pole and is "blue."
  6-8. The earth's magnetism undergoes changes. These changes consist of the following:

Diurnal Changes

  6-9. These are daily changes which are caused by the movement of the magnetic poles in an orbit having a diameter of about 50 miles.

Annual Changes

  6-10. These simply represent the yearly permanent changes in the earth's magnetic field.

Secular Changes

  6-11. These are changes which occur over a period of years.

Figure 6-1. Earth's Magnetic Field


  6-12. The magnetic compass onboard ship may be classified or named according to its location or use. The magnetic compass located in a position favorable for taking bearings and used in navigation is called the standard compass. The magnetic compass at the steering station (used normally for steering or as a standby when the steering gyro repeater fails) is called the steering compass. Direction from either of these instruments must be labeled as "per standard compass" or "per steering compass" for identification.
  6-13. The following components make up a standard 7 1/2-inch Navy compass (Figure 6-2). The (7 1/2 inches refers to the diameter of the compass.

Figure 6-2. Components of the 7 1/2-inch Navy Compass

Magnets (A)
  6-14. These are four (two in older compasses) cylindrical bundles of magnetic steel wire or bar magnets which are attached to the compass card to supply directive force. Some newer compasses have a circular magnet made of a metallic alloy.
Compass Card (B)
  6-15. This is an aluminum disc, graduated in degrees from 0° to 360° . It also shows cardinal and intercardinal points. North is usually indicated by the fleur de lis figure in addition to the cardinal point. Being attached to the magnets, the compass card provides a means of reading direction.
Compass Bowl (C)
  6-16. This is a bowl-shaped container of nonmagnetic material (brass) which serves to contain the magnetic elements, a reference mark, and the fluid. Part of the bottom may be transparent (glass) to permit light to shine upward against the compass card.
Fluid (D)
  6-17. This is liquid surrounding the magnetic element. According to Archimedes principle of buoyancy, a reduction of weight results in a reduction of friction, making possible closer alignment of the compass needle with the magnetic meridian. Any friction present will tend to prevent complete alignment with the magnetic meridian. Today's compasses contain a highly refined petroleum distillate similar to Varsol, which increases stability and efficiency and neither freezes nor becomes viscous at low temperatures.
Float (E)
  6-18. This is an aluminum, air-filled chamber in the center of the compass card. This further reduces weight and friction at the pivot point.
Expansion Bellows (F)
  6-19. This is an arrangement in the bottom of the compass bowl. This operates to keep the compass bowl completely filled with liquid, allowing for temperature changes. A filling screw facilitates addition of liquid, which may become necessary notwithstanding the expansion bellows.
Lubber Line
  6-20. This is a reference mark on the inside of the compass bowl. It is aligned with the ship's fore and aft axis or keel line of the ship. The lubber line is a reference for the reading of direction from the compass card. The reading of the compass card on the lubber line at any time is the "ship's heading."
  6-21. This is a metal ring on two pivots in which the compass bowl is placed. The compass is also on two pivots which permits it to tilt freely in any direction and remain almost horizontal in spite of the ship's motion. The compass rests on the binnacle. An important concept is that regardless of the movement of the ship, the compass card remains fixed (unless some magnetic material is introduced to cause additional deviation from the magnetic meridian). The ship, the compass bowl, and the lubber line move around the compass card. To the observer witnessing this relative motion, it appears that the compass card moves.
  6-22. The following characteristics of the magnetic compass limit its direction-finding ability:
  • Sensitive to any magnetic disturbance.
  • Useless at the magnetic poles and is sluggish and unreliable in areas near the poles.
  • Deviation (explained later) changes as a ship's magnetic properties change. The magnetic properties also change with changes in the ship's structure or magnetic cargo.
  • Deviation changes with heading. The ship as well as the earth may be considered as a magnet. The effect of the ship's magnetism upon the compass changes with the heading.
  • Does not point to true north.
  6-23. Compass error, defined as the angular difference between the compass direction and the corresponding true direction, may be easily computed since it is the algebraic sum of variation and deviation (Figure 6-3). Compass error must be applied to the compass direction to get true direction and must be applied to true direction, with a reversal of the sign, to arrive at compass direction.
  6-24. Variation is found recorded within the compass rose or direction reference of the chart in use. Deviation is found by consulting the deviation card that provides the deviation for each 15° of magnetic heading.

Figure 6-3. Compass Error

  6-25. Because the magnetic north pole and the true North Pole are not located at the same point, the magnetic compass does not seek true north. The magnetic compass aligns itself with the magnetic meridian. The angular difference between the magnetic meridian and the true meridian is called "variation" because it varies at different points on the earth's surface (Figure 6-4). Even in the same locality it usually does not remain constant, but increases or decreases annually at a certain known rate.

Figure 6-4. Magnetic Variation

  6-26. The variation for any given locality, together with the amount of annual increase or decrease, is shown on the compass rose of the chart for that particular locality. The "compass rose" (Figure 6-5) indicates that in 1964 there was a 14° 45' westerly variation in that area, increasing 2' annually. To find the amount of variation in this specific locality, determine how many years have elapsed since 1964, multiply that number by the amount of annual increase, and add that sum to the variation in 1964. You add it in this example, because it is an annual increase. If it were decreasing, you would subtract it. Variation normally is rounded off to the nearest 0.5° .
  6-27. Variation remains the same for any heading of the ship at a given locality. No matter which direction the ship is heading, the magnetic compass, if affected by variation only, points steadily in the general direction of the magnetic north pole. Remember, always use the compass rose that is closest to the area in which you are located.

Figure 6-5. Compass Rose

  6-28. The magnetic properties of a ship cause deviation in the magnetic compass. Ship magnetism is of two types:
  • Permanent. Magnetism in steel or hard iron that acts as a permanent magnet.
  • Induced. Magnetism of soft iron, which is only temporary and is constantly changing depending upon ship's heading and latitude.
  6-29. The most convenient method of determining deviation, and the one most commonly used, is to check the compass on each 15o heading against a properly functioning gyrocompass. Because the ship must be on a magnetic heading when determining deviation, gyro error and local variation must be applied to each gyro heading.
  6-30. It is a simple process to station personnel at each magnetic compass and have them record the amount of deviation for each compass upon signal from an observer at the gyrocompass or repeaters.
  • Compare with a magnetic compass of known deviation. This method is similar to comparison with a gyrocompass except that it is not necessary to know the local variation. This method is used frequently by ships not equipped with gyrocompasses.
  • Determine deviation of the magnetic compass by a range. Figure 6-6 shows how to determine deviation of the compass by a range.

Figure 6-6. How to Determine Deviation of the Compass by a Range

Figure 6-6. How to Determine Deviation of the Compass by a Range (continued)

  6-31. Deviation is not the same on every heading. Therefore, the deviation that exists on the various headings must be recorded so the correction for compass error will be known. Use a process called "swinging ship" to determine and record the deviation your ship is headed through every 15° of the compass. The ship is steadied on each 15° . The navigator usually is stationed at the standard compass and ship's personnel are stationed at the other magnetic compasses. As the ship steadies upon one of the 15° increments of the compass and the compasses settle down, the navigator gives the signal to record the deviation on that heading. When the process of swing ship is completed and the deviation for the 24 headings recorded, the deviations are transferred to a deviation card as shown (Figure 6-7).
  6-32. The deviation card contains important information that is necessary for future compass adjustment as well as for computing compass error.

Figure 6-7. Sample Deviation Card

  6-33. Before a final recording is posted on the deviation card, a simple graph is made to plot the recorded deviations (Figure 6-8). This graph will quickly show if the deviation found for each of the 24 headings is consistent. When each of the deviations is plotted on the graph, a line connecting the points should form a smooth curve. Do not expect all points to be on the smooth curve, but they should be close. If you find one heading way off (2° -1 or 3° ), go back and check the deviation on that heading again.
  6-34. To compute the deviation on any magnetic heading not given in the table, it is necessary to interpolate between the two nearest recorded readings. If the deviations recorded on each 15° heading do not vary by more than 1/2° from the adjacent readings, you may use the deviation for the heading nearest the one you are checking.

Figure 6-8. Deviation Graph

  6-35. Variation and deviation combined constitute "magnetic compass error." The course on which you want the ship to make good is the true course, selected from the compass between two points on a chart. Knowing the true course, it is necessary for you to find the compass course that you must steer to make good that true course. Compass course is found by applying the compass error, in terms of variation and deviation, to the true course.
  6-36. Your problem could be the other way around. Suppose you have a bearing taken by magnetic compass. Plotting true bearings on the chart is preferable to plotting magnetic compass bearings. Therefore, you must apply variation and deviation to the compass bearing to obtain the true bearing.
  6-37. Changing from true course to compass course, or vice versa, may be accomplished more easily by means of this handy ditty: Can Dead Men Vote Twice? Write each word of the ditty in column form, then opposite each word set down what it represents, as shown in Table 6-1.

Table 6-1. Word Ditty











  6-38. The problem will always be either (knowing the true course) to work up the line to the compass course, or (knowing the compass course) to work down the line to the true course. Going up the line, or changing from true to compass, is called "uncorrecting." Coming down the line, or changing from compass to true, is called "correcting." Remember this rule: When correcting, ADD easterly and SUBTRACT westerly error. When uncorrecting, SUBTRACT easterly and ADD westerly error. All compass errors, whether due to variation or deviation, are either easterly or westerly. There are no northerly or southerly errors.
  6-39. Now work a problem. Suppose the true course is 000° and you want to know the course to steer by magnetic compass. You are uncorrecting. Write the initial letters of each word of the ditty in a line as follows:

  6-40. You already know what T is, so write it down as follows:

  6-41. Do the following if the chart shows a variation of 11° E.

  6-42. When uncorrecting, remember that you subtract easterly and add westerly errors. The 11° is an easterly variation so subtract it from 360° to get a magnetic course of 349° . Write that down as follows:

  6-43. Sometimes you need to know a magnetic heading or bearing. If that were all you were looking for in this example, you could stop right here. However, you want to go on and find the compass course. Let us say the deviation table shows a deviation of 14° W for a 349° heading. Write that down as follows:

  6-44. When uncorrecting, you add westerly error, so add 14° to 349° and get 003° . Now you have the following:

  Note: Therefore, in order to head 000° true, you must steer 003° by this particular magnetic compass.
  6-45. Note in the sample problem that the easterly variation and westerly deviation almost canceled each other, leaving an error of only 3° W. If you do not want to go through the correction process in detail, you can find the algebraic sum of the errors beforehand. This advance preparation is accomplished by subtracting the lesser from the greater, if they are unlike, or adding them if they are alike. Then you can apply the result directly to either T or C, depending on whether you are correcting or uncorrecting.
  6-46. We were uncorrecting this time--changing from true to compass. We could have used the same method to change from compass to true. Remember, when correcting, add easterly and subtract westerly errors.


  6-47. In determining position and safely conducting a ship from one position to another, the navigator uses a variety of piloting instruments. The correct use of these instruments and the ability to interpret properly the information obtained from these instruments require skill and experience.
  6-48. Piloting instruments must be capable of considerable accuracy. One of the best known navigational instruments is the magnetic compass, which is used for the measurement of direction. Aside from the compass, piloting equipment falls under the following categories:
  • Bearing-taking devices.
  • Speed-measuring devices (includes distance and time).
  • Depth-measuring devices.
  • Plotting instruments.
  • Miscellaneous instruments.
  6-49. Instruments used for taking bearings consist of a azimuth circle, telescopic alidade, and pelorus (or dumb compass).
Azimuth Circle
  6-50. This is a nonmagnetic metal ring (Figure 6-9). It is sized to fit a 7 1/2-inch compass bowl or a gyro repeater. The inner lip is marked in degrees from 0° to 360° counterclockwise for measuring relative bearings. The azimuth circle is fitted with two sighting vanes. The forward or far vane has a vertical wire and the after or near vane has a peep sight. Two finger lugs are used to position the instrument while aligning the vanes. A hinged reflector vane mounted at the base and beyond the forward vane is used for reflecting stars and planets when observing azimuths. Beneath the forward vane are mounted a reflecting mirror and the extended vertical wire.
  6-51. This lets the mate read the bearing or azimuth from the reflected portion of the compass card. For taking azimuths of the sun, an additional reflecting mirror and housing are mounted on the ring, each midway between the forward and after vanes. The sun's rays are reflected by the mirror to the housing, where a vertical slit admits a line of light. This admitted light passes through a 45o reflecting prism and is projected on the compass card from which the azimuth is directly read. In observing both bearings and azimuths, two attached spirit levels are used to level the instrument. An azimuth circle without the housing and spare mirror is called a bearing circle.

Figure 6-9. Azimuth Circle

Telescopic Alidade
  6-52. This is similar to a bearing circle, only it has a telescope attached to the metal ring instead of the forward and after sight vanes (Figure 6-10). The magnifying power of the telescope lens makes distant objects appear more visible to the observer. When looking through the telescope, the bearing may be read, since the appropriate part of the compass card is reflected by a prism in the lower part of the field of vision. When a ship is yawing badly, it is easy to lose sight of an object using the telescopic alidade because the field of vision is very limited.

Figure 6-10. Telescopic Alidade

Pelorus (Dumb Compass)
  6-53. In a ship without gyro installation, a pelorus or "dumb compass" (Figure 6-11) is located on either bridge wing, from which bearings may be taken on objects visible from the ship. The gyro repeaters has replaced the pelorus on all gyro-equipped ships.
  6-54. The pelorus consists of a nonmagnetic metal ring mounted in gimbals on a pelorus stand. The inner lip of the ring is graduated through 360° . The 000° mark corresponds to the ship's lubber line.
  6-55. Inside the ring is a dumb compass card. The card can be rotated so as to bring any heading on the lubber line. A pair of sighting vanes, mounted on the card, are aimed at the object whose bearing is desired.
  6-56. If the dumb compass card is set to the ship's true course, the bearing by pelorus will be a true bearing, provided the ship is exactly on course at the instant the bearing is taken. This synchronization seldom happens, however, and it is customary for the person taking the bearing to yell out "Mark!" the instant he takes it and simultaneously clamps the sighting vanes. The steersman notes the compass heading when he hears "Mark". If the ship was on the true heading, the bearing obtained was a true bearing. If she was off course, a correction equal to the amount she was off must be applied to the bearing. If the course was by magnetic compass, the bearing by pelorus must still be converted from compass to true.
  6-57. Relative bearings are taken by pelorus merely by setting the dumb compass card's 000° heading to the lubber line.

Figure 6-11. Pelorus

  6-58. Speed can be determined indirectly by means of distance and time or it can be measured directly. All instruments in common use for measuring speed determine the rate of motion through the water.
  6-59. An engine room counter counts off the number of revolutions the propeller shaft turns. When the unit of time is known, speed can be determined. Pitch is the distance that a given propeller would advance in one complete revolution if it were working against a solid. The difference between the pitch and the actual distance advanced through water is known as slip, expressed as a percentile. Therefore, if a propeller has a pitch of 10 feet and turns 200 revolutions per minute, it advances 2,000 feet per minute, which is equivalent to 19.75 knots. Assuming this propeller has a slip of 18 percent, the ship's speed is reduced by this amount. This is known as positive slip. So, instead of 19.75 knots, the speed is only 19.75 X 0.82 = 16.2 knots.
  6-60. Depth-measuring devices may be classified as mechanical or electronic. The mechanical type is represented by the hand lead. The most common example of an electronic type is the fathometer.

Hand Lead

  6-61. The hand lead line (Figure 6-12) is the oldest and most reliable depth-finding device for shallow depths. It consists of a lead weight (7 to 14 pounds) attached to a 20-fathom line marked as follows:

2 fm

2 strips of leather

3 fm

3 strips of leather

5 fm

white rag

7 fm

red rag

10 fm

leather with hole

13 fm

same as 3 fm

15 fm

same as 5 fm

17 fm

same as 7 fm

20 fm

line with two knots

Figure 6-12. Hand Lead Line

  6-62. Swing the hand lead in a pendulum motion to produce momentum for two complete turns. Then let it go to allow the lead to sink ahead of the chains (station on ship from which soundings are taken). The leadsmen call out depths referring to definite markings as "by the mark . . ." and other depth values as "by the deep . . ." Phraseology for fractions are "and a half," "and a quarter," or "a quarter less" as appropriate; for example, "and a half five" (5 1/2 fm) or "a quarter less four" (3 3/4 fm). The lead line should be measured and marked when wet. A hollow indentation in the end of the lead permits "arming". Arming is the application of tallow or other sticky substance to the lead in order to sample the bottom to determine the type of bottom you are over.
Type Fathometer or Echo Sounder
  6-63. This is an electronic device that emits a sound signal and measures the time between the emission of the signal and the return of the echo. Since the signal must travel to the bottom and return, the depth is half the distance traveled, considering the average speed of sound waves in water to be 800 fathoms (4,800 feet) per second. When using the fathometer, remember that the fathometer sends the signal from the keel. All depths shown on the fathometer are depths under the keel. The actual depth is equal to the sum of the depth under the keel and the draft of the ship. Fathometers are usually found on category A-3 vessels.
  6-64. The most basic of plotting instruments is the pencil, preferably a No. 2 or No. 3 pencil. Keep all lines short, and print legibly and lightly for easy erasure. Art gum erasers are normally used for erasure since art gum is less destructive to chart surfaces than India red rubber erasers.
Navigator's Kit
  6-65. This kit contains a drawing compass, dividers, and screwdriver (for adjusting points), all essential navigation instruments. Dividers are used to measure distance and the drawing compass is useful for constructing circles and arcs such as circular LOPs and arcs of visibility (Figure 6-13).

Figure 6-13. Divider/Drawing Compass

Parallel Rules
  6-66. These are simple devices for plotting direction. The rules consist of two parallel bars with parallel cross braces of equal length which form equal opposite angles (Figure 6-14). The rules are laid on the compass rose (direction reference of a chart) with the leading edge aligning the center of the rose and the desired direction on the periphery of the rose. Holding first one bar and moving the second, then holding the second and moving the first, parallel motion is ensured. Lines representing direction may be plotted as desired upon the chart.

Figure 6-14. Parallel Rules

  6-67. A pair of plastic triangles can also be used for transferring a direction from one part of a chart to another, although not for great distances (Figure 6-15). The two triangles need not be similar in size or shape. The two hypotenuses (longest sides) are placed together, and one of the other sides of one triangle is lined up with the course or bearing line or with the desired direction at the compass rose. The other triangle is held firmly in place as a base, and the first one is slid along in contact with it, carrying the specified line to a new position while maintaining its direction. If necessary, the triangles may be alternately held and slid for moving somewhat greater distances. Two right triangles may be used in conjunction with a compass rose as a means for plotting direction.

Figure 6-15. Triangles

Drafting Machine or Parallel Motion Protractor
  6-68. This plotting device is anchored to the chart table and consists of two links and a drafting arm (Figure 6-16). An elbow between the two links permits unrestricted movement. Between the outboard link and the drafting arm, a metal disc is graduated as a protractor. It permits orientation of the protractor with the chart. A setscrew, usually on the inner edge, is loosened when in use to permit movement of the drafting arm in any given direction. Tighten the setscrew before plotting. The advantage of the drafting machine over other plotting instruments is speed.

Figure 6-16. Drafting Machine

  6-69. The following are essential to have aboard ship. Ensure that the are in good working order.
  6-70. In selecting a pair of binoculars, keep in mind that increased power and magnification results in a narrowing field of view. A set of 7 X 50 binoculars is recommended for marine use. The "7" indicates the power of magnification and the "50" indicates the diameter of the front lens in millimeters. Minor adjustment to one eyepiece permits separate focusing for each eye. The glass lenses are usually coated to reduce the glare. Additional filters are available for further glare reduction. Binoculars must be handled with care and properly stowed when not in use. The lenses should be cleaned often, using only lens paper to prevent damage to the polished surfaces.
  6-71. In selecting a flashlight, ensure that it is water resistant and that it is designed to withstand shocks and also seals out moisture. The case should be made of non-slip rubber. A red plastic disc should be inserted in the lighted end to provide a red light for sustaining your night vision or to prevent unnecessarily lighting up the bridge at night.


  6-72. Aids to navigation are put at various points along the coasts and navigable waterways as markers and guides to help mariners determine their position. They also serve to warn of hidden dangers and assist in making landfall when approaching from the high seas. They also provide a continuous chain of charted marks, showing improved channels and assisting in coastal piloting.
  6-73. Aids to navigation consist of lighthouses, light towers, minor lights, buoys, day beacons, and ranges. A ship cannot suspend piloting operations because of darkness. For this reason, aids to navigation are lighted whenever it is necessary and practical. Therefore, you must be knowledgeable of the light characteristics of the aids to navigation.
  6-74. A light has distinctive characteristics which distinguish it from other lights or convey specific information. A light may show a distinctive sequence of light and dark intervals. A light may also display a distinctive color or color sequence.
Color of Lights
  6-75. For all buoys in the lateral system having lights, the following system of color is used:
  • Green Lights. Used only on those buoys marking the left-hand side of a channel returning from seaward (black, odd-numbered buoys) or on red-and-black, horizontally banded buoys having the topmost band painted black.
  • Red Lights. Used only on those buoys marking the right-hand side of a channel when entering from sea (red, even-numbered buoys) or on red-and-black, horizontally banded buoys having a red topmost band.
  • White Lights. May be used on either side of channels instead of red or green lights. White lights are frequently used where greater visibility is desired, such as at a change in the direction of the channel. No special significance is derived from a white light, the purpose of the buoy being indicated by its color, number, or its light phase characteristic.
Fixed, Flashing, and Occulting Lights
  6-76. Some navigational lights are fixed, meaning that they burn steadily. Most important lights, however, go through repeated periods of systematic changes of light and darkness. It is this characteristic of a navigational light that is most valuable for identification purposes.
  6-77. The following are the principal characteristics of lights on lighthouses. Lighted buoys have a few more special characteristics, which are mentioned later.
  • Flashing. A single flash showing at regular intervals, the duration of light always being less than the duration of darkness.
  • Occulting. A light totally eclipsed at regular intervals, the duration of light always being greater than the duration of darkness.
  • Fixed and Flashing. A fixed light varied at regular intervals by groups of two or more flashes of greater brilliance. The group may, or may not, be preceded and followed by an eclipse.
  • Group Flashing. Groups of two or more flashes showing at regular intervals.
  • Group Occulting. A light with a group of two or more eclipses at regular intervals.
  • Equal Interval (Isophase). A single flash with the duration of light equal to that of darkness.
  • Morse Code. Light in which flashes of different durations are grouped to produce a Morse character or characters.
  • Alternating. Rhythmic lights which exhibit different colors during each sequence.
  6-78. The visibility of lights is measured by the specific distance, in nautical miles, a navigator can expect to see a lighthouse or beacon. In speaking of the visibility of a light, the following terms apply:
  • Geographic Range. This is the maximum calculated distance at which the curvature of the earth permits a light to be seen from a height of eye of 15 feet above the water when the elevation of the light is taken above the height datum.
  • Luminous Range. This is the maximum distance at which a light can be seen under present visibility conditions. This luminous range does not take into account of the elevation of the light, the observer's height of eye, the curvature of the earth, or interference from background lighting. The luminous range is determined from the known nominal luminous range (called the nominal range) and the present visibility conditions.
  • Nominal Range. This is the maximum distance at which a light can be seen in clear weather as defined by the International Visibility Code (meteorological visibility of 10 nautical miles).
  • Computed Visibility. This is determined for a particular light, taking into account its elevation, nominal range, height of eye of the observer, and the curvature of the earth.
  6-79. The computed visibility will not exceed the light's nominal range (luminous range) or the computed range. Although, under certain atmospheric conditions, the loom of a powerful light may appear before the light itself is visible. The following examples illustrate the procedure for determining the visibility of a light.
  Example 1: Determine the visibility of a light that is 90 feet above sea level for an observer with a height of eye of 50 feet.
  Solution: From the DMAHTC List of Lights, determine the nominal range (20 miles) and the height of the light above water (90 feet).
  Determine horizon distance from Table 6-2, and place in form shown below.
  Height of eye of 50 feet 8.1 miles  
  Height of light above water, 90 feet 10.9 miles  
  Computed visibility 19.0 miles  
  Nominal range 20.0 miles  
  Answer: 19.0 miles  
  Example 2: Determine the visibility of another light that is 77 feet above sea level for an observer with height of eye of 37 feet.
  Solution: From the DMAHTC List of Lights, determine the nominal range (10 miles) and the height of the light above water (77 feet). Determine horizon distance from Table 6-1, interpolating for 77 feet.
  Height of eye of 37 feet 7.0 miles  
  Height of light above water, 77 feet 10.0 miles  
  Computed visibility 17.0 miles  
  Nominal range 10.0 miles  
  Answer: 10.0 miles  

Table 6-2. Table of Distance of Visibility of Objects at Sea

The following table gives the approximate geographic range of visibility for an object that may
be seen by an observer whose eye is sea level. Therefore, in practice, it is necessary to add
to these a distance of visibility corresponding to the height of the observer's eye above sea level.








































































































































































































































  6-80. Lighthouses (Figure 6-17) are located on all coasts of the US, on the Great Lakes, and along many interior waterways. They are placed wherever a powerful light may be of assistance to navigators or wherever a danger requires a warning beacon of long-range visibility. Visibility of a powerful light increases with height. Therefore, the principal purpose of a light structure is to increase the height of a light above sea level.
  Note: It should also be remembered that a light placed at a great elevation is often obscured by clouds, mist, and fog than one near sea level.
  6-81. A lighthouse may also contain fog-signaling and radio beacon equipment. Many lights formerly operated by keepers are now automatic. Lighthouses still staffed by keepers may also contain living quarters. When operating personnel are housed in separate buildings grouped around the tower, the group of buildings is called a light station.
  6-82. Secondary, minor, and automatic lights are located in structures ranging from towers that resemble important seacoast lighthouses down to a small cluster of piles supporting a battery box and lens.
  6-83. Solid colors, bands, stripes, and other color patterns are applied to lighthouses and light structures as an aid to identification. Minor structures sometimes are painted red or black, like channel buoys, to indicate the side of the channel on which they are located--red structures to the right, black to the left, returning seaward.

Figure 6-17. Lighthouse

  6-84. A typical light tower (Figure 6-18) deckhouse is 60 feet above the water, 80 feet square, and supported by steel legs in pilings driven nearly 300 feet into the ocean bottom. The deckhouse accommodates living quarters and radio-beacon, communications, and oceanographic equipment. The top serves as a landing platform that will take the largest helicopters flown by the Coast Guard. On one corner of the deckhouse is a 32-foot radio tower supporting the radio-beacon antenna and a 3 1/2 million-candlepower light. At an elevation of 130 feet above the water it is visible for 18 miles. The construction details of other towers will vary slightly, but all are of the same general type.

Figure 6-18. Light Tower

  6-85. Sectors of red glass are placed in the lanterns of certain lighthouses to indicate an area in which a ship will be in danger of running on rocks, shoals, or some other hazard. The arcs over which the red light shows, are the danger sectors whose bearings usually appear on the chart (Figure 6-19). Although the light is red within the danger bearings, its other characteristics remain the same.
  6-86. Sectors may be only a few degrees in width, marking an isolated obstruction, or they may be so wide that they extend from the direction of deep water to the beach. In most instances, red sectors indicate water to be avoided. A narrow green sector may signify a turning point or the best water across a shoal. Exact significance of each sector may be obtained from the chart.
  6-87. All sector bearings are true bearings in degrees, running clockwise around the light as a center. As shown in Figure 6-19, the bearings of the red sector from the light are 135° to 178° . This sector is defined in the Light List in terms of bearings from the ship. These bearings are 315° to 358° , the reciprocals of the preceding bearings. The light shown in the diagram would be defined as follows: obscured from land to 315° , red thence to 358° , green thence to 050° , white thence to land.
  6-88. On either side of the line of demarcation between colored and white sectors, there is always a small sector of undefined color because the edges of a sector cannot be cut off sharply in color. Under some atmospheric conditions, a white light itself may have a reddish appearance. Therefore, light sectors must not be relied upon entirely, but position must be verified repeatedly by bearings taken on the light itself or other fixed objects.

Figure 6-19. Light Sectors

  6-89. Navigational buoys are moored floating markers. Place them so that they can guide ships in and out of channels, warn them away from hidden dangers, lead them to anchorage areas, and so forth. Buoys may be of various sizes and shapes (Figure 6-20). However, regardless of their shapes, their distinctive coloring is the chief indication of their purposes.

Figure 6-20. Types of Buoys

  6-90. Although a buoy's type has no special navigational significance, it may help toward its identification from the description given in Table 6-3. The following are the principal types of buoys:
Spar Buoys
  6-91. These are large logs, trimmed, shaped, and appropriately painted. Although the Coast Guard has now eliminated them, spar buoys may still be found in some foreign or private systems of aids.
Can and Nun Buoys
  6-92. The shape of can buoys are cylindrical. The shape of nun buoys are conical.
Bell Buoys
  6-93. These have flat tops, surmounted by a framework supporting a bell. Older bell buoys are sounded by the motion of the sea. Newer types are operated automatically by compressed gas or electricity.
Gong Buoys
  6-94. These are similar to bell buoys except that they have a series of gongs, each with a different tone.
Whistle Buoys
  6-95. These are similar to bell buoys except they carry a whistle sounded by the sea's motion or horns that are sounded at regular intervals by mechanical or electrical means.
Lighted Buoys
  6-96. These carry batteries or gas tanks and are surmounted by a framework supporting a light. A description of the lights on lighted buoys is given later.
Combination Buoys
  6-97. These are buoys in which a light and sound signal are combined, such as a lighted bell, gong, or whistle buoy.
  6-98. In the US, red buoys mark the right side and black buoys mark the left side of the channel, coming from seaward. A great help in remembering this placement of buoys is the jingle "red right returning."
  6-99. Normally red channel buoys are cone-shaped nun buoys, whereas black channel buoys are cylindrical can buoys. This situation probably is the only one in which a buoy's shape is of any significance, and even here the rule is not controlling. It is the color that counts. Sometimes red and black buoys are painted white on top, but this color scheme is merely to enable them to be located more easily at night.

Table 6-3. Buoy Characteristics

































  6-100. Red and black, horizontally banded buoys mark junctions in the channel, wrecks, or obstructions that may be passed on either side. If the topmost band is black, the preferred channel will be followed by keeping the buoy on the port (left) side. If the topmost band is red, the preferred channel will be followed by keeping the buoy on the starboard (right) side.
  Note: When proceeding toward seaward, it may not be possible to pass on either side of these buoys, and the chart should always be consulted.
  6-101. Black and white, vertically striped buoys mark the middle of a channel or fairway. Yellow buoys mark quarantine anchorages.
  6-102. The foregoing conditions are practically all the colors on buoys that have a direct connection with navigation. Buoys painted all white have no special significance; they have uses not concerned with navigation, such as marking ordinary anchorage areas. Buoys with black and white horizontal stripes are used in some locations to mark fish trap areas. A white buoy with a green top usually means a dredging area.
  6-103. The red buoys marking the right side of a channel bear even numbers, starting with the first buoy from seaward. This maritime situation is perhaps the only one in which anything to starboard has an even number. Black channel buoys, to the left of the channel coming from seaward, have odd numbers (Figure 6-21). Both the number and one or two letters appear on some channel buoys, for example, the Governor's Island (New York Harbor) West End Shoal Bell Buoy. Because it is the first buoy on the port side of the channel coming from seaward, it is painted black and carries the number 1. The letters "GI" are painted next to the 1.
  6-104. Banded or striped buoys are not numbered, but some have letters for identification purposes. For example, the East Rockaway Inlet Bell Buoy (vertical black and white stripes) carries the letters "ER."

Figure 6-21. Numbered Buoys

  6-105. Red lights are used only on red buoys or red and black horizontally banded buoys with the topmost band red. Green lights are only for black buoys or black and red horizontally-banded buoys with the topmost band black. When a brighter light is required, a white light frequently is substituted for either the green or the red light. White lights are the only lights used on the black and white, vertically striped buoys that mark the middle of a channel or fairway. Characteristics of lights on lighted buoys are as follows:
  • A Fixed (Steady) Light. This light indicates a black or red channel buoy.
  • A Flashing Light. This light which flashes at regular intervals (not more than 30 flashes per minute) may also indicate a black or red buoy or a special-purpose buoy.
  • A Quick-Flashing Light. This light with no fewer than 60 flashes per minute, is also found on a black or red buoy, but it is used at a turning point or junction where special caution is required or to mark wrecks that can be passed only on one side.
  • An Interrupted, Quick-Flashing Light. This light which has repeated series of quick flashes, separated by about 4-second dark intervals, indicates a red and black, horizontally banded obstruction buoy that can be passed on either side.
  • A Short-Long Flashing Light. This light which flashes Morse code "A" (a short and a long flash, recurring at the rate of about 8 per minute) is placed on a black and white, vertically striped midchannel buoy and may be passed on either side. This will always be a white light.
  6-106. Unlighted aids to navigation (except unlighted buoys) are called "day beacons." A day beacon may consist of a single pile with a daymark on top of it, a spar supporting a cask, a slate or masonry tower, or any of several structures.
  6-107. Day beacons, like lighthouses and light structures, usually are colored to distinguish them from their surroundings and make them easy to identify. Day beacons marking channels are colored and numbered like channel buoys. Many are fitted with reflectors that show the same colors a lighted buoy would show at night in the same position.
  6-108. Two day beacons, located some distance apart on a specific true bearing, constitute a "day beacon range." Two lights, similarly located, are a "lighted range." When a ship reaches a position where the two lights or beacons are seen exactly in line, she is "on the range" (Figure 6-22). Ranges are especially valuable for guiding ships along the approaches to or through narrow channels. Much steering through the Panama Canal is done on ranges.
  6-109. Lights on ranges may show any of the three standard colors, and they may be fixed, flashing, or occulting. Most range lights appear to lose brilliance rapidly as a ship diverges from the range line of bearing.
  6-110. When steering on a range, it is important to be sure the limit beyond which the range line of bearing cannot be followed safely. This information is available on the chart.

Figure 6-22. Range Lights

  6-111. Most lighthouses have installed fog-signaling apparatus, ordinarily sounded by mechanical means. For identification purposes, each station has its own assigned number of blasts, recurring at specified intervals. A definite time is required for each station to sound its entire series of blasts, and this timing provides another means of identification.
  6-112. The various types of apparatus produce a corresponding variance of pitch and tone. This gives your ear a chance to compare the sound of a station with its description in the Light List.
  6-113. The Intracoastal Waterway is a channel through which light-draft vessels can navigate coastwise from the Chesapeake Bay almost to the Mexican border, remaining inside natural or artificial breakwaters for most of the trip. The following paragraphs describe special markings for the Intracoastal Waterway proper and for those portions of connecting or intersecting waterways that must be crossed or followed in navigating it.
  6-114. Every buoy, day beacon, or light structure along the Intracoastal Waterway has part of its surface painted yellow, the distinctive coloring adopted for this waterway. Lighted buoys have a band or border of yellow somewhere.
  6-115. As you proceed from the Chesapeake Bay toward Mexico, red buoys and day beacons are to the right and black buoys are to the left. As in other channels, red buoys have even numbers; black buoys, odd numbers. Because the numbers would increase excessively in such a long line of buoys, the buoys are numbered in groups of no more than 200. At certain natural dividing points, numbering begins again at 1.
  6-116. Lights on buoys in the Intracoastal Waterway follow the standard system of red or white lights on red buoys and green or white lights on black buoys. Lights on lighted aids other than buoys also agree with the standard rules for lights on aids to navigation.
  6-117. In the lateral buoyage system used on all navigable waters of the US, the coloring, shape, and lighting of buoys indicate the direction of a danger relative to the course that should be followed. The color, shape, lights, and number of buoys in the lateral system as used by the US are determined relative to a direction from seaward. Some countries using the lateral system color their buoys and lights the direct opposite of the US color scheme. Before going into foreign waters, consult the Sailing Directions for an exact description of the aids to navigation in the particular locality.
  6-118. In offshore channels, the lateral buoyage system prescribes the following markings and colorings for US waters:
  • Proceeding in a southerly direction along the Atlantic coast.
  • Proceeding in a northerly and westerly direction along the Gulf coast.
  • Proceeding in a northerly direction along the Pacific coast is considered to be proceeding from seaward.
  Accordingly, coastal buoys on the right, when proceeding in those directions, are red buoys with even numbers. On the Great Lakes, offshore buoys are colored and numbered from the outlet of each lake toward its upper end. The Intracoastal Waterway is marked from the North Atlantic states to the lower coast of Texas, regardless of the compass bearings of individual sections.


  6-119. This is moving the vessel's position on a chart from a known position, using the course (or courses) steered and the speed (or speeds) through water (Figure 6-23). No allowance is made for wind, current, waves, and poor steering.

Figure 6-23. Course Line, Track, Course Over Ground, Course Made Good, and Heading

  6-120. The following are some familiar terms used when using dead reckoning:
  6-121. The horizontal direction in which the ship points or heads at any given second, expressed in angular units clockwise from 000° through 360° . The heading of the ship is also called ship's head. The heading is always changing as the ship swings or yaws across the course line due to the seas or steering error.
  6-122. As applied to marine navigation, the direction in which a vessel is to be steered or is being steered, and the direction of travel through the water. The course is measured from 000° clockwise from the reference direction to 360° . Course may be designated as true, magnetic, compass, or grid as determined by the reference direction.
DR Track Line
  6-123. In marine navigation, the graphic representation of a ship's course normally used in the construction of a dead reckoning plot.
  6-124. The ordered rate of travel of a ship through the water is normally expressed in knots. In some areas where distances are stated in statute miles, such as on the Great Lakes, speed units will be "miles per hour." Speed is used in conjunction with time to establish a distance run on each of the consecutive segments of a DR plot.
  6-125. A position established at a specific time to a high degree of accuracy. It may be determined by any of a number of methods. A running fix is a position of lesser accuracy, based in part on present information and in part on information transferred from a prior time.
DR Position
  6-126. A position determined by plotting a vector or series of consecutive vectors using only the true course and distance determined by speed through the water, without considering current.
Estimated Position
  6-127. The more probable position of a ship, determined from incomplete data or data of questionable accuracy. In practical use, it is often the DR position modified by the best additional information available.
Dead Reckoning Plot
  6-128. Commonly called DR plot. In marine navigation it is the graphical representation on the nautical chart of the line or series of lines, which are the vectors of the ordered true courses and distance run on these courses at the ordered speeds while proceeding from a fixed point. The DR plot originates at a fix or running fix; it is suitably labeled as to courses, speeds, and times of various dead reckoning positions, usually at hourly intervals or at times of change of course or speed. A DR plot properly represents courses and speeds that have been used. A similar plot may be made in advance for courses and speeds that are expected to be used.
Estimated Time of Departure
  6-129. The estimate of the time of departure from a specified location according to a scheduled move to a new location.
  6-130. The DR track (or DR track line) is the path or course the ship is expected to follow. It is plotted from a known position using courses and speeds through water. When plotting a DR track, no consideration is given for current and wind. Therefore, a path the ship actually follows may be quite different from the one plotted due to offsetting influences discussed later in this chapter.
  6-131. There are three basic principles you must follow when plotting a DR track:
  • A DR track is ALWAYS started from a known position.
  • Only true courses are plotted.
  • Only speed through water is used for determining distance traveled.
  6-132. The purpose of the DR track is to show the navigator basically where he is planning to go, the rate of advance, and the ETA at various points along the way and at the final destination. After the DR track has been plotted, the navigator determines whether or not the basic track is clear of navigational hazards, as well as deciding what navigational aids are available and when they are visible. By examining the DR track, all elements of danger and surprise are eliminated for the voyage. If the navigator finds a DR track is going to lead into shoal waters or unnecessary danger, the DR track can be reevaluated in sufficient time to prevent any hazard to the ship.
  6-133. When plotting the DR track, be sure that all DR tracks and distances are accurately measured. Neatness is essential to avoid confusion and error. Overlong lines and unnecessarily written information cause errors. Completeness of the DR track is necessary to show course, times, and positions. Standardization of labeling ensures neatness and clarity for any person using that plot.
  6-134. The course is the intended horizontal direction of travel. This DR track starts from a known position and is plotted as follows:
  6-135. Above and parallel to the course line, place a capital C and three digits to indicate the true course (C 007° ). It is customary to label courses to the nearest whole degree. Under the course line and below the direction label, place a capital S and two digits for the speed. Since the course is given in degrees true and speed in knots, it is not necessary to indicate the units or reference direction.
  6-136. DR positions are marked along the track line at specific time intervals depending upon where the ship is being navigated. In confined areas such as rivers and bays, DR plots can be plotted for every 15 minutes or half hour. Running along the coast in less restrictive waters, the DR plots can be put in every hour; and, when sailing great distances over open waters, they can be plotted every 4 hours. DR plots are put in wherever a course or speed change occurs. The standard symbols used are shown in Table 6-4. A new DR track is plotted from a well established fix. Even though an estimated position is shown, you do not begin a new DR track from this point.
  6-137. Figure 6-24 shows the times of fixes, estimated positions, and the times of dead reckoning positions. Time of fixes and estimated positions are placed horizontally while the times of dead reckoning positions are placed other than horizontally.
  6-138. A DR track is based on an assumption of making good an exact course and speed. There are many factors prevailing against the ship to prevent this. Some of these factors are poor steering and the inability to make good the plotted speed, current, and leeway.
  6-139. Additional terms that must be understood in regards to dead reckoning include:
  6-140. This is the horizontal motion of water. The direction in which the water is moving is called the set and the velocity of the flow is called the drift.
  6-141. This is the intended horizontal direction of travel with respect to the earth, taking into consideration known or predicted offsetting effects such as current, wind, and seas.
Speed of Advance
  6-142. This is the intended speed with respect to the earth, taking into consideration the effect of known or predicted current. SOA is also used to designate the average speed that must be made good to arrive at a destination at a specified time.
  6-143. This is the direction toward which the current is flowing. If the broader definition of "current" is used, the resultant direction is of all offsetting influences. Note carefully that the description of the set of a current is directly opposite from the naming of a wind--a westerly current sets toward the west, a westerly wind blows from the west.

Table 6-4. Standard Plotting Symbols









Figure 6-24. Labeling a DR Track

  6-144. This is the speed of a current (or the speed of the resultant of all offsetting influences), usually stated in knots. However, some publications, notably pilot charts and atlases, express drift as nautical miles per day.
Course Made Good
  6-145. CMG is the resultant direction from a given point of departure to a subsequent position. It is the direction of the net movement from one point to another, disregarding any intermediate course changes en route. This will differ from the track if the correct allowance for current was not made.
Speed Made Good
  6-146. SMG is the net speed based on distance and time of passage directly from one point to another, disregarding any intermediate speed change. SMG is speed along the CMG.
Course Over The Ground
  6-147. COG is the actual path of the vessel with respect to the earth. This may differ from CMG if there are intermediate course changes, steering inaccuracies, varying offsetting influences, and so forth. In current sailing triangles, CMG (not COG) is used.
Speed Over The Ground
  6-148. SOG is the ship's actual speed with respect to the earth along the COG. In current sailing, SMG (not SOG) is used.
  6-149. In navigation, it is customary to use the word "current" to include all factors that introduce geographical error in dead reckoning. When a fix is obtained, one assumes that the current has set from the DR position at the same time as the fix and the drift equals the distance in miles between these two positions divided by the hours since the last fix. This is true, regardless of the number of changes of course and speed since the last fix.
  6-150. If set and drift can be estimated, a better position is obtained by applying the correction to the DR position. This is referred to as an estimated position. If a current is setting in the same direction as the course of the ship or its reciprocal, the course made good is the same, only the speed changes. If course and set are in the same direction, the speeds are added. If in opposite directions, the smaller speed is subtracted from the larger. This is a common situation for ships encountering tidal currents when entering or leaving port.
  6-151. For ships crossing a current, three current vector diagrams can be made giving the information needed to determine speed and courses to be steered. These diagrams can be made on scrap paper or an area on the plotting sheet away from the actual plot.
  Example 1: Find course and speed made good through a current with ship's speed 10 knots, course 080° , current set 140° , and drift 2 knots (Figure 6-25).
  Solution: From point A draw the line AB. This represents the course and speed (080° at 10 knots) in length.
  From B draw in BC, the set and drift of the current, 140° at 2 knots. The direction and length of AC are the estimated course made good (089° ) and speed made good (11.2 knots).

Figure 6-25. Find Course and Speed Made Good

  Example 2: Determine the course to steer at a given speed to make good a desired course with this information: ship's speed 12 knots, the desired course 095° , the current's set 170° , and the drift 2.5 knots (Figure 6-26).
  Solution: From point A draw course line AB extending in the direction of 095° (indefinite length).
  From point A draw in the current line AC for the set 170° and drift 2.5 knots. Using C as a center, take the dividers, swing an arc of radius (ship's speed 12 knots) CD, intersecting the line AB at D. Measure the direction of line CD (083° .5). This is the course to steer. Measure the length of the line AD; 12.4 knots is the speed made good.

Figure 6-26. Find Course to Steer and Speed Made Good

  Example 3: Determine what course and speed you must proceed in order to make a desired course and a desired speed good with this information: desired course 265° , desired speed to be made good 15 knots, current set of 185° , and a drift of 3 knots (Figure 6-27).
  Solution: From A draw line AB in the direction to be made good (265° ) and for a length equal to the speed to be made good (15 knots).
  From A draw AC, the set and drift of the current, 185° and 3 knots.
  Draw a line from C to B. The direction of this line is 276° ; this is the course to be steered. The length of the line equals the speed required (14.8 knots).
  6-152. These current vectors can be made to any convenient scale and at any convenient place such as the center of the compass rose, unused area of the plotting sheet, a separate sheet of paper, or directly on the plot.
  6-153. These current vectors can be made to any convenient scale and at any convenient place such as the center of the compass rose, unused area of the plotting sheet, a separate sheet of paper, or directly on the plot.
  6-154. Leeway is the leeward motion of a vessel due to wind. It may be expressed as distance, speed, or angular difference between the course steered and the course made good through the water. The amount of leeway depends upon the speed and relative direction of the wind, type of vessel, exposed freeboard, trim, state of the sea, and depth of water. Leeway is most conveniently applied by adding its effect to that of the current and other elements introducing geographical error in the dead reckoning.

Figure 6-27. Course to Steer

  6-155. All piloting and maneuvering solutions contain three factors: time, speed, and distance. When piloting you should be able to figure in your head any one of the three factors. The following are two simple methods that you can use.
The 3-Minute Rule
  6-156. This is an excellent method for computing time, speed, and/or distance, when working in an area where short distances are involved or the times between measurements are close together. The 3-minute rule is: the distance, in yards, traveled by a ship in 3 minutes is equal to the speed of the ship multiplied by 100.

  Example 1: A ship travels 1,500 yards in 3 minutes. What is the ship's speed?

  Example 2: A ship's speed is 15 knots. How far will it travel in 3 minutes?

  When you have determined the distance traveled in 3 minutes, you can further determine the distance traveled in 1 minute by dividing the distance by 3.
The 60-Minute Rule
  6-157. This method for computing time, speed, or distance requires that you know two factors in order to determine the third:

  As an aid, use this diagram:

  1. Cover the unknown with your finger.
  2. Multiply by the opposites on the diagram.
  3. Divide by the remaining figure on the diagram for the answer.
  Example 1: A ship travels 7 miles in 30 minutes. What is its speed?

  Example 2: A ship's speed is 15 knots. How far will it travel in 20 minutes?

  Example 3: A ship's speed is 8 knots. How long will it take for it to travel 6 miles?


  6-158. Piloting is a method of determining position and directing the movements of a vessel by reference to landmarks, navigational aids, or soundings. Piloting is usually used as a primary means of navigation when entering or leaving port and in coastal navigation. In piloting, the navigator obtains warnings of danger, fixes the position frequently and accurately, and determines the proper course of immediate action.
  6-159. An LOP is a line at some point of which a ship may be presumed to be on, as a result of observation or measurement (Figure 6-28). When piloting, LOPs are used to fix a ship's position. An LOP is determined with reference to a landmark, which must be correctly identified, and its position must be shown on the chart which is in use. There are three general types of LOPs: ranges, bearings including tangents, and distance arcs.
  Note: An LOP should not be drawn through charted aids on the chart, because after a few erasures these symbols will become very difficult or impossible to see.

Figure 6-28. Lines of Position

  6-160. A ship is on "range" when two landmarks are observed to be in line. This range is represented on a chart by means of a straight line which, if extended, would pass through the two related chart symbols. This line, labeled with the time expressed in four digits (above the line), is a fix of the ship's position. It should be noted that the word "range" in this context differs significantly from its use as a synonym of distance.
  6-161. It is preferable to plot true bearings, although either true or magnetic bearings may be plotted. Therefore, when the relative bearing of a landmark is observed, it should be converted to true bearing or direction by the addition of the ship's true heading. Since a bearing indicates the direction of a terrestrial object from the observer, a LOP is plotted from the landmark in a reciprocal direction. For example, if a lighthouse bears 300° , the ship bears 120° from the lighthouse. A bearing LOP is labeled with the time expressed in four digits above the line and the bearing in three digits below the line (Figure 6-29).

Figure 6-29. Plotting

  6-162. A special type of bearing is the tangent. When a bearing is observed on the right-hand edge of a projection of land, the bearing is a right tangent. A bearing on the left-hand edge of a projection of land as viewed by the observer is a left tangent. A tangent provides an accurate LOP if the point of land is sufficiently abrupt to provide a definite point for measurement. It is inaccurate, for example, when the slope is so gradual that the point for measurement moves horizontally with the tide.
  6-163. A distance arc is a circular LOP. When the distance from an observer to a landmark is known, the fix of the observer's position is a circle with the landmark as center having a radius equal to the distance. The entire circle need not be drawn, since in practice the navigator normally knows his position with sufficient accuracy as to require only the drawing of an arc of a circle. The arc is labeled with the time above expressed in four digits and the distance below in nautical miles (and tenths). The distance to a landmark may be measured using radar, the stadimeter, or the sextant in conjunction with TABLES 9 and 10 of the American Practical Navigator.
  6-164. A fix is defined as a point of intersection of two or more simultaneously obtained LOPs. The symbol for a fix is a small circle around the point of intersection. It is labeled with the time expressed in four digits. Fixes may be obtained using the following combinations of LOPs:
  • A line of bearing or tangent and a distance arc.
  • Two or more lines of bearing or tangents.
  • Two or more distance arcs.
  • Two or more ranges.
  • A range and a line of bearing or tangent.
  • A range and a distance arc.
  Figure 6-30 shows how to take a fix using the azimuth circle.
  6-165. Since two circles may intersect at two points, two distance arcs used to obtain a fix are not undesirable. The navigator in making his choice between two points of intersection may however, consider an approximate bearing, sounding, or his DR position. When a distance arc of one landmark and a bearing of another are used, the navigator may again be faced with the problem of choosing between two points of intersection at the same location.
  6-166. Three considerations in selecting landmarks or other aids for obtaining LOPs are:
  • Angle of intersection.
  • Number of objects.
  • Permanency.
  6-167. Two LOPs crossing at nearly right angles will result in a fix with a smaller amount of error than two LOPs separated by less than 30° . If there is a small compass error or a slight error is made in reading the bearings, the resulting discrepancy will be less in the case of the fix produced by widely separated LOPs than the fix from LOPs separated by only a few degrees.
  6-168. If only two landmarks are used, any error in observation or identification may not be apparent. With three or more LOPs, each LOP acts as a check. If all intersect in a pinpoint or form a small triangle, you may generally rely on the fix. Where three LOPs are used, a spread of 60° would result in optimum accuracy.
  6-169. When selecting landmarks or other aids, preference should be given to permanent structures such as lighthouses or other structural and natural features identifiable ashore or in shallow water. Buoys, while very convenient, are less permanent and may drift from their charted position because of weather and sea conditions or through maritime accident.
  6-170. The navigator often has no choice of landmarks or their permanency, number, or spread. In such cases he must use whatever is available, no matter how undesirable. In the evaluation of his fix, the number of landmarks, their permanency, and their spread should receive consideration. When three LOPs cross forming a triangle, it is difficult to determine whether the triangle is the result of a compass error or an erroneous LOP. The plotting of four LOPs usually indicates if a LOP is in error.
  6-171. It is not always possible for the navigator to observe LOPs simultaneously. Sometimes only one landmark is available. The navigator may make frequent observations of the one landmark, or he may, after one observation, lose sight of the available landmark only to sight a new navigational aid. If the navigator is able to compute distances during these observations, he may easily establish his fix. If not, or if for any reason his data consists of LOPs obtained at different times, then he may establish a position that only partially takes into account the current. This position is the running fix, identified by the same symbol as the fix except that the time label is followed by the abbreviation "R. FIX." It is better than a DR position, but less desirable than a fix.

Figure 6-30. Taking a Fix Using the Azimuth Circle

Figure 6-30. Taking a Fix Using the Azimuth Circle (continued)

  6-172. A running fix is established by advancing the first LOP in the direction of travel of the ship (the course), a distance equal to the nautical miles the ship should have traveled during the interval between the time of the first LOP and the time of the second LOP. The point of intersection of the first LOP as advanced and the second LOP is the running fix. The advanced LOP is labeled with the times of the two LOPs separated by a dash and the direction, above and below the line respectively (Figure 6-31).

Figure 6-31. Bearing LOP Advanced

  6-173. Use one of the following methods if the ship changes course and/or speed between observations:
Perpendicular Method
  6-174. After two LOPs are obtained, plot DR positions corresponding to the lines of the LOPs. Drop a perpendicular from the earlier DR to the earlier LOP. At the second DR, make a line having the same direction and length as the first perpendicular. At the end of the latter line, make a line parallel to the original LOP (this is the advanced LOP). The intersection of this advanced LOP and the last observed LOP establishes the running fix. The following is the logic of the perpendicular method. The ship's speed and course generates the DR track line. If the advanced LOP lies with respect to the second DR position as it previously lay with respect to the old DR, then it has been advanced parallel to itself a distance and a direction consistent with the ship's movement during the intervening time. A variation of this method is to construct, instead of a perpendicular, a line of any direction between the first DR and LOP. This line is then duplicated at the second DR and the LOP advance as before. In duplication, the line from the second DR must be the same length and direction as the line connecting the first DR and LOP (Figure 6-32).
Course Made Good Method
  6-175. As in the perpendicular method, plot DR positions to match the time labels of the LOPs. Connect the DR positions. The connecting line represents the course and distance that the ship should have made good. Advance the first LOP a distance and direction corresponding to the line connecting the two DR positions (Figure 6-33).

Figure 6-32. Perpendicular Method

Figure 6-33. Course Made Good Method

  6-176. The running fix may be a well-determined position and is usually considered as such. For this reason the DR track is normally replotted using the running fix as a new point of origin.
  6-177. However, a running fix does not fully account for current, and the displacement of the running fix from the DR is not a true indication of current. If a head current is expected, extra allowance should be made for clearance of dangers to be passed abeam, because the plot of running fixes based upon any single landmark near the beam will indicate the ship to be farther from that danger than it actually is. If a following current is experienced, then the opposite condition will exist. This occurs because the actual distance made good is less with a head current and greater with a following current than the distance the LOP is advanced based upon dead reckoning. A limitation of 30 minutes should be imposed on the elapsed time between LOPs in a running fix.
  6-178. It is possible to keep a ship in safe water without frequent fixes through the use of danger bearings. Figure 6-34 shows a shoal that presents a hazard to navigation, a prominent landmark at point A, and a ship proceeding along the coastline on course BC. To construct a danger bearing, line AX is drawn from point A tangent to the outer edge of the danger. If the bearing of point A remains greater than the danger bearing, the ship is in safe water, as with YA and ZA. The reverse is true when the danger is to port; the danger angle must remain greater than the angle to point A.

Figure 6-34. Danger Bearing

  6-179. Wind or current could set the ship toward the shoal. However, even before a fix could be taken, this situation would be indicated by repeated bearings of point A.
  6-180. A position obtained by sounding is usually approximate. Accuracy of this type of position depends on the following:
  • How completely and accurately depths are indicated on the chart.
  • The irregularity of the depths.
  It is impossible to obtain a position by soundings if the ship is located in an area where depth is uniform throughout. In practice, position by soundings ordinarily serves as a check on a fix taken by some other means.
  6-181. Suppose you have only one spot on or near your DR track where water depth is 6 fathoms and the depth over the rest of the area for miles around is 20 fathoms. If you record 6 fathoms, you can be certain you are located at the one point where a 6-fathom depth was shown on the chart.
  6-182. Piloting by soundings is not that simple. Figure 6-35 gives you an idea of the principle involved. What you really do is get a contour of the bottom you are passing over and try to match it up with a similar contour shown by the depth figures on the chart. One of the best methods is to proceed as follows:
  6-183. Draw a straight line on a piece of transparent paper or plastic. Calculate how far apart your soundings will be, in other words, the length of the ship's run between soundings and mark off distances on the line to the scale of the chart. Alongside each mark representing a sounding, record the depth obtained at that sounding. The line represents the ship's course. The line of soundings recorded on the overlay should fit the depth marks on the chart somewhere near your DR track. If it makes an accurate fit, it probably is a close approximation of the course the ship is actually making good.

Figure 6-35. Line of Soundings

  6-184. A running fix can be obtained by using the mathematical relationships involved as shown in Figure 6-36. A ship is steaming past lighthouse D. At point A, a bearing of D is observed and expressed as degrees right or left of the course (a relative bearing if the ship is on course). At a later time at point B, a second bearing is taken of D and expressed the same as before. At point C, the lighthouse is broad on the beam. The angles at A, B, and C are known, as are the distances between these points. Trigonometry can be used to find the distance from D at any bearing. Distance and bearing provide fix.

Figure 6-36. A Running Fix

  6-185. A quick easy solution can be provided by using the extract of TABLE 7 from Pub. No. 9, American Practical Navigator (Vol. II) (Figure 6-37). To determine the distance of an object as a vessel steams past, observe two bearings of the object, note the time interval between the bearings, and determine the distance run. Determine the angular difference between the course and the first bearing and the angular difference between the course and the second bearing. Using the extract of TABLE 7, find the difference in degrees between the course and the first bearing going across the top of the table to that degree. Then go down that column until you come to the degrees of difference between the course and the second bearing. Multiply the distance run between bearings by the number in the first column to find the distance of the object at the time of the second bearing and then by the number in the second column to find the distance when you come abeam.

Figure 6-37. Extract of Table 7 - Distance of an Object by Two Bearings

  Note: The solution from TABLE 7, as with any of the "special cases," is accurate only if a steady course has been steered, the vessel has been unaffected by the current, and the speed used is the speed over the ground.
  6-186. Applying the data from Figure 6-37, locate the difference between the course and the first bearing (angle B, A, and D in Figure 6-36) along the top of the table. Also locate the difference between the course and the second bearing (angle C, B, and D) at the left of the table. For each pair of angles listed, two numbers are given. To find the distance from the lighthouse at the time of the second bearing (B and D), multiply the distance run between A and B by the first number from the table. To find the distance off when you will be abeam (C and D), multiply the distance run between A and B by the second number in the table. If the distance between A and B is 1 mile, then the tabulated values are the distances sought. The tables are computed for even degrees. If a degree difference is an odd number, then you interpolate.
  Example: Using the problem shown in Figure 6-36, the course is 050° , the speed is 15 knots, the first bearing of the lighthouse at 1130 was 024° , and the second bearing of the lighthouse at 1140 was 359° .
  Required: The distance the ship was off at 1140 at the second bearing and the distance off when abeam.
  Solution: The distance run between the first and second bearing:

  6-187. The difference between the course and the first bearing is 26° (050° - 024° ). The difference between the course and the second bearing is 51° (050° + 360° - 359° ). From TABLE 7 the two numbers (factors) are 1.04 and 0.81. This is found by interpolation between 50° and 52° for the second bearing.
  6-188. Distance from lighthouse at second bearing:

1.04 X 2.5 = 2.6 miles.

  6-189. Distance off lighthouse when abeam:

0.81 X 2.5 = 2.0 miles.


  6-190. Certain combinations of angles provide a quick mental solution without the use of TABLE 7. These are referred to as special cases and include bow-and-beam bearings and doubling the angle on the bow.
Bow-and-Beam Bearings
  6-191. When the bearing of an object diverges 45° from the ship's heading, it is said to be "broad on the bow." When the angle increases to 90° , it is said to be "on the beam." By noting the time of the first bearing and the time when the bearing is on the beam, you mentally compute the distance run. The distance run is equal to the distance off when abeam. The distance run equals the distance abeam because 45° and 90° angles provide a right triangle with equal sides. The advantage of the bow-and-beam bearing is the ease of solution (Figure 6-38).

Figure 6-38. Bow and Beam Method

Doubling the Angle on the Bow
  6-192. There are two special cases to remember: the 7/10 rule and the 7/8 rule.
  • The 7/10 rule. If the first bearing is 22° .5 from the ship's heading and the second bearing is 45° on the bow, the distance the object will pass abeam is about 7/10 of the distance run between bearings.
  • The 7/8 rule. If the angles are 30° and 60° , the distance of the object when abeam is about 7/8 of the distance run between bearings.
  6-193. When there is only one object on which bearings can be taken, another method known as "two-bearings-and-run-between" is used. A bearing is taken of the object as the ship proceeds on its course. After the angle has changed by at least 30° , a second bearing is taken. This second bearing is taken before or after the object has passed abeam. The distance run is determined for the time that has elapsed between bearings (Figure 6-39).
  6-194. Both bearings are plotted on the chart as shown in Figure 6-39. The dividers are opened to the distance run between the two bearings and are moved parallel to the course line until the points of the dividers fall on the bearing lines. The divider's points show the positions of the ship at the times of the first and second bearings. The accuracy of this procedure is dependent on the following factors:
  • Estimation of ship's speed.
  • Accuracy of steering between bearings.
  • Current.
  • Accuracy of the bearings themselves.
  Accuracy of these factors at the time you are taking these bearings determines the reliability of the position. At best, it is still considered as an estimated position rather than a fix.

Figure 6-39. Two-Bearings-and-Run-Between


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