Chapter 1 introduction to marine navigation definitions 100. The Art And Science Of Navigation

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100. The Art And Science Of Navigation

Marine navigation blends both science and art. A good navigator gathers information from every available source, evaluates this information, determines a fix, and compares that fix with his pre-determined “dead reckoning” position. A navigator constantly evaluates the ship’s position, anticipates dangerous situations well before they arise, and always keeps “ahead of the vessel.” The modern navigator must also understand the basic concepts of the many navigation systems used today, evaluate their output’s accuracy, and arrive at the best possible navigational decisions.

Navigation methods and techniques vary with the type of vessel, the conditions, and the navigator’s experience. Navigating a pleasure craft, for example, differs from navigating a container ship. Both differ from navigating a naval vessel. The navigator uses the methods and techniques best suited to the vessel and conditions at hand.

Some important elements of successful navigation can- not be acquired from any book or instructor. The science of navigation can be taught, but the art of navigation must be developed from experience.

101. Types Of Navigation

Methods of navigation have changed through history. Each new method has enhanced the mariner’s ability to complete his voyage safely and expeditiously. One of the most important judgments the navigator must make in- volves choosing the best method to use. Commonly recognized types of navigation are listed below.

Dead reckoning (DR) determines position by advancing a known position for courses and distances. A position so determined is called a dead reckoning (DR) position. It is generally accepted that only course and speed determine the DR position. Correcting the DR position for leeway, current effects, and steering error result in an estimated position (EP). An inertial navigator develops an extremely accurate EP.

Piloting involves navigating in restricted waters with frequent determination of position relative to geographic and hydrographic features.

Celestial navigation involves reducing celestial measurements to lines of position using tables, spherical trigonometry, and almanacs. It is used primarily as a backup to satellite and other electronic systems in the open ocean.

Radio navigation uses radio waves to determine position by either radio direction finding systems or hyperbolic systems.

Radar navigation uses radar to determine the distance from or bearing of objects whose position is known. This process is separate from radar’s use as a collision avoidance system.

Satellite navigation uses artificial earth satellites for determination of position.

Electronic integrated bridge concepts are driving future navigation system planning. Integrated systems take inputs from various ship sensors, electronically display positioning information, and provide control signals required to maintain a vessel on a preset course. The navigator be- comes a system manager, choosing system presets, interpreting system output, and monitoring vessel response.

In practice, a navigator synthesizes different methodologies into a single integrated system. He should never feel comfortable utilizing only one method when others are available for backup. Each method has advantages and dis- advantages. The navigator must choose methods appropriate to each particular situation.

With the advent of automated position fixing and electronic charts, modern navigation is almost completely an electronic process. The mariner is constantly tempted to rely solely on electronic systems. This would be a mistake. Electronic navigation systems are always subject to failure, and the professional mariner must never forget that the safety of his ship and crew may depend on skills that differ little from those practiced generations ago. Proficiency in conventional piloting and celestial navigation remains essential.

102. Phases Of Navigation

Four distinct phases define the navigation process. The 12 INTRODUCTION TO MARINE NAVIGATION

mariner should choose the system mix that meets the accu- racy requirements of each phase.

Inland Waterway Phase: Piloting in narrow canals, channels, rivers, and estuaries.

Harbor/Harbor Approach Phase: Navigating to a harbor entrance and piloting in harbor approach channels.

Coastal Phase: Navigating within 50 miles of the coast or inshore of the 200 meter depth contour.

OceanPhase:Navigatingoutsidethecoastalareain the open sea.

The navigator’s position accuracy requirements, his fix interval, and his systems requirements differ in each phase. The following table can be used as a general guide for se- lecting the proper system(s).

Inland Harbor/Harbor Coastal Ocean Waterway Approach


Piloting Celestial Radio Radar X X X Satellite X* X X X



Table 102. The relationship of the types and phases of navigation. * Differential GPS may be used if available.


103. Important Conventions And Concepts

Throughout the history of navigation, numerous terms and conventions have been established which enjoy world- wide recognition. The professional navigator, to gain a full understanding of his field, should understand the origin of certain terms, techniques, and conventions. The following section discusses some of the important ones.

Defining a prime meridian is a comparatively recent development. Until the beginning of the 19th century, there was little uniformity among cartographers as to the meridi- an from which to measure longitude. This did not lead to any problem because there was no widespread method for determining longitude accurately.

Ptolemy, in the 2nd century AD, measured longitude eastward from a reference meridian 2 degrees west of the Canary Islands. In 1493, Pope Alexander VI established a line in the Atlantic west of the Azores to divide the territo- ries of Spain and Portugal. For many years, cartographers of these two countries used this dividing line as the prime meridian. In 1570 the Dutch cartographer Ortelius used the easternmost of the Cape Verde Islands. John Davis, in his 1594 The Seaman’ s Secrets, used the Isle of Fez in the Ca- naries because there the variation was zero. Mariners paid little attention to these conventions and often reckoned their longitude from several different capes and ports during a

voyage. The meridian of London was used as early as 1676, and

over the years its popularity grew as England’s maritime in- terests increased. The system of measuring longitude both east and west through 180°may have first appeared in the middle of the 18th century. Toward the end of that century, as the Greenwich Observatory increased in prominence, En- glish cartographers began using the meridian of that observatory as a reference. The publication by the Observa- tory of the first British Nautical Almanac in 1767 further entrenched Greenwich as the prime meridian. An unsuc- cessful attempt was made in 1810 to establish Washington, D.C. as the prime meridian for American navigators and car- tographers. In 1884, the meridian of Greenwich was officially established as the prime meridian. Today, all mar- itime nations have designated the Greenwich meridian the prime meridian, except in a few cases where local references are used for certain harbor charts.

Charts are graphic representations of areas of the earth for use in marine or air navigation. Nautical charts depict features of particular interest to the marine navigator. Charts have probably existed since at least 600 BC. Stereo- graphic and orthographic projections date from the 2nd century BC. In 1569 Gerardus Mercator published a chart using the mathematical principle which now bears his name. Some 30 years later, Edward Wright published cor-


rected mathematical tables for this projection, enabling cartographers to produce charts on the Mercator projection. This projection is still widely in use.

Sailing directions or pilots have existed since at least the 6th century BC. Continuous accumulation of naviga- tional data, along with increased exploration and trade, led to increased production of volumes through the Middle Ages. “Routiers” were produced in France about 1500; the English referred to them as “rutters.” In 1584 Lucas Waghenaer published the Spieghel der Zeevaerdt (The Mariner’ s Mirror), which became the model for such pub- lications for several generations of navigators. They were known as “Waggoners” by most sailors. Modern pilots and sailing directions are based on extensive data collec- tion and compilation efforts begun by Matthew Fontaine Maury beginning in 1842.

The compass was developed about 1000 years ago. The origin of the magnetic compass is uncertain, but Norse- men used it in the 11th century. It was not until the 1870s that Lord Kelvin developed a reliable dry card marine com- pass. The fluid-filled compass became standard in 1906.

Variation was not understood until the 18th century, when Edmond Halley led an expedition to map lines of variation in the South Atlantic. Deviation was understood at least as early as the early 1600s, but correction of com- pass error was not possible until Matthew Flinders discovered that a vertical iron bar could reduce errors. Af- ter 1840, British Astronomer Royal Sir George Airy and later Lord Kelvin developed combinations of iron masses and small magnets to eliminate most magnetic compass error.

The gyrocompass was made necessary by iron and steel ships. Leon Foucault developed the basic gyroscope in 1852. An American (Elmer Sperry) and a German (Anshutz Kampfe) both developed electrical gyrocompasses in the early years of the 20th century.

The log is the mariner’s speedometer. Mariners origi- nally measured speed by observing a chip of wood passing down the side of the vessel. Later developments included a wooden board attached to a reel of line. Mariners measured speed by noting how many knots in the line unreeled as the ship moved a measured amount of time; hence the term knot. Mechanical logs using either a small paddle wheel or a rotating spinner arrived about the middle of the 17th cen- tury. The taffrail log still in limited use today was developed in 1878. Modern logs use electronic sensors or spinning devices that induce small electric fields propor- tional to a vessel’s speed. An engine revolution counter or shaft log often measures speed onboard large ships. Dop- pler speed logs are used on some vessels for very accurate speed readings. Inertial and satellite systems also provide highly accurate speed readings.

The Metric Conversion Act of 1975 and the Omnibus Trade and Competitiveness Act of 1988 established the metric system of weights and measures in the United States. As a result, the government is converting charts to

the metric format. Considerations of expense, safety of nav- igation, and logical sequencing will require a conversion effort spanning many years. Notwithstanding the conver- sion to the metric system, the common measure of distance at sea is the nautical mile.

The current policy of the Defense Mapping Agency Hydrographic/Topographic Center (DMAHTC) and the National Ocean Service (NOS) is to convert new compila- tions of nautical, special purpose charts, and publications to the metric system. This conversion began on January 2, 1970. Most modern maritime nations have also adopted the meter as the standard measure of depths and heights. How- ever, older charts still on issue and the charts of some foreign countries may not conform to this standard.

The fathom as a unit of length or depth is of obscure origin. Posidonius reported a sounding of more than 1,000 fathoms in the 2nd century BC. How old the unit was then is unknown. Many modern charts are still based on the fath- om, as conversion to the metric system continues.

The sailings refer to various methods of mathematical- ly determining course, distance, and position. They have a history almost as old as mathematics itself. Thales, Hippar- chus, Napier, Wright, and others contributed the formulas that permit computation of course and distance by plane, traverse, parallel, middle latitude, Mercator, and great cir- cle sailings.

104. The Earth

The earth is an oblate spheroid (a sphere flattened at the poles). Measurements of its dimensions and the amount of its flattening are subjects of geodesy. However, for most navigational purposes, assuming a spherical earth introduc- es insignificant error. The earth’s axis of rotation is the line connecting the North Pole and the South Pole.

A great circle is the line of intersection of a sphere and a plane through its center. This is the largest circle that can be drawn on a sphere. The shortest line on the surface of a sphere between two points on the surface is part of a great circle. On the spheroidal earth the shortest line is called a geodesic. A great circle is a near enough approximation to a geodesic for most problems of navigation. A small circle is the line of intersection of a sphere and a plane which does not pass through the center. See Figure 104a.

The term meridian is usually applied to the upper branch of the half-circle from pole to pole which passes through a given point. The opposite half is called the lower branch.

A parallel or parallel of latitude is a circle on the surface of the earth parallel to the plane of the equator. It connects all points of equal latitude. The equator is a great circle at latitude 0°. See Figure 104b. The poles are single points at latitude 90°. All other parallels are small circles.



Figure 104a. The planes of the meridians meet at the polar axis.

105. Coordinates

Coordinates, termed latitude and longitude, can de- fine any position on earth. Latitude (L, lat.) is the angular distance from the equator, measured northward or south- ward along a meridian from 0°at the equator to 90°at the poles. It is designated north (N) or south (S) to indicate the direction of measurement.

The difference of latitude (l, DLat.) between two places is the angular length of arc of any meridian between their parallels. It is the numerical difference of the latitudes if the places are on the same side of the equator; it is the sum of the latitudes if the places are on opposite sides of the equator. It may be designated north (N) or south (S) when appropriate. The middle or mid-latitude (Lm) between two places on the same side of the equator is half the sum of their latitudes. Mid-latitude is labeled N or S to indicate whether it is north or south of the equator.

The expression may refer to the mid-latitude of two places on opposite sides of the equator. In this case, it is equal to half the difference between the two latitudes and takes the name of the place farthest from the equator. How- ever, this usage is misleading because it lacks the significance usually associated with the expression. When the places are on opposite sides of the equator, two mid-lat- itudes are generally used. Calculate these two mid-latitudes by averaging each latitude and 0°.

Longitude (l, long.) is the angular distance between

Figure 104b. The equator is a great circle midway between the poles.

the prime meridian and the meridian of a point on the earth, measured eastward or westward from the prime meridian through 180°. It is designated east (E) or west (W) to indi- cate the direction of measurement.

The difference of longitude (DLo) between two plac- es is the shorter arc of the parallel or the smaller angle at the pole between the meridians of the two places. If both places are on the same side (east or west) of Greenwich, DLo is the numerical difference of the longitudes of the two places; if on opposite sides, DLo is the numerical sum unless this ex- ceeds 180°, when it is 360°minus the sum. The distance between two meridians at any parallel of latitude, expressed in distance units, usually nautical miles, is called departure (p, Dep.). It represents distance made good east or west as a craft proceeds from one point to another. Its numerical value between any two meridians decreases with increased latitude, while DLo is numerically the same at any latitude. Either DLo or p may be designated east (E) or west (W) when appropriate.

106. Distance On The Earth

Distance, as used by the navigator, is the length of the rhumb line connecting two places. This is a line making the same angle with all meridians. Meridians and parallels which also maintain constant true directions may be consid- ered special cases of the rhumb line. Any other rhumb line spirals toward the pole, forming a loxodromic curve or


107. Direction On The Earth

Figure 106. A loxodrome

loxodrome. See Figure 106. Distance along the great circle connecting two points is customarily designated great-cir- cle distance. For most purposes, considering the nautical mile the length of one minute of latitude introduces no sig- nificant error.

Speed (S) is rate of motion, or distance per unit of time. A knot (kn.), the unit of speed commonly used in navigation, is a rate of 1 nautical mile per hour. The expression speed of advance (SOA) is used to indicate the speed to be made along the intended track. Speed over the ground (SOG) is the actual speed of the vessel over the surface of the earth at any given time. To calculate speed made good (SMG) be- tween two positions, divide the distance between the two positions by the time elapsed between the two positions.

Direction is the position of one point relative to another s. Navigators express direction as the angular difference in degrees from a reference direction, usually north or the ship’s head. Course (C, Cn) is the horizontal direction in which a vessel is steered or intended to be steered, ex- pressed as angular distance from north clockwise through 360°. Strictly used, the term applies to direction through the water, not the direction intended to be made good over the ground.

The course is often designated as true, magnetic, com- pass, or grid according to the reference direction. Track made good (TMG) is the single resultant direction from the point of departure to point of arrival at any given time. Course of advance (COA) is the direction intended to be made good over the ground, and course over ground (COG) is the direction between a vessel’s last fix and an EP. A course line is a line drawn on a chart extending in the direction of a course. It is sometimes convenient to express a course as an angle from either north or south, through 90°or 180°. In this case it is designated course angle (C) and should be properly labeled to indicate the origin (prefix) and direction of measurement (suffix). Thus, C N35°E = Cn 035°(000°+ 35°), C N155°W = Cn 205°(360°- 155°), C S47°E = Cn 133°(180°- 47°). But Cn 260°may be either C N100°W or C S80°W, depending upon the conditions of the problem.

Track (TR) is the intended horizontal direction of travel with respect to the earth. The terms intended track and trackline are used to indicate the path of intended trav- el. See Figure 107a. The track consists of one or a series of course lines, from the point of departure to the destination, along which it is intended to proceed. A great circle which a vessel intends to follow is called a great-circle track, though it consists of a series of straight lines approximating a great circle.

Figure 107a. Course line, track, track made good, and heading.



Heading (Hdg., SH) is the direction in which a vessel is pointed, expressed as angular distance from 000°clock- wise through 360°. Do not confuse heading and course. Heading constantly changes as a vessel yaws back and forth across the course due to sea, wind, and steering error.

Bearing (B, Brg.) is the direction of one terrestrial point from another, expressed as angular distance from 000°(North) clockwise through 360°. When measured through 90°or 180°from either north or south, it is called bearing angle (B). Bearing and azimuth are sometimes used interchangeably, but the latter more accurately refers to the horizontal direction of a point on the celestial sphere from

a point on the earth. A relative bearing is measured relative to the ship’s heading from 000°(dead ahead) clockwise through 360°. However, it is sometimes conveniently mea- sured right or left from 0°at the ship’s head through 180°. This is particularly true when using the table for Distance of an Object by Two Bearings.

To convert a relative bearing to a true bearing, add the true heading:

True Bearing = Relative Bearing + True Heading. Relative Bearing = True Bearing – True Heading.

Figure 107b. Relative Bearing.


108. Latitude And Longitude Determination

Navigators have made latitude observations for thou- sands of years. Accurate sun declination tables have been published for centuries, enabling experienced seamen to compute latitude to within 1 or 2 degrees. Mariners still use meridian observations of the sun and highly refined ex-me- ridian techniques. Those who today determine their latitude by measuring the altitude of Polaris are using a method well known to 15th century navigators.

A method of finding longitude eluded mariners for centuries. Several solutions independent of time proved too cumbersome. The lunar distance method, which determines GMT by observing the moon’s position among the stars, became popular in the 1800s. However, the mathematics re- quired by most of these processes were far above the

abilities of the average seaman. It was apparent that the so- lution lay in keeping accurate time at sea.

In 1714, the British Board of Longitude was formed, offering a small fortune in reward to anyone who could pro- vide a solution to the problem.

An Englishman, John Harrison, responded to the chal- lenge, developing four chronometers between 1735 and 1760. The most accurate of these timepieces lost only 15 seconds on a 156 day round trip between London and Bar- bados. The Board, however, paid him only half the promised reward. The King finally intervened on Harri- son’s behalf, and Harrison received his full reward of £20,000 at the advanced age of 80.

Rapid chronometer development led to the problem of determining chronometer error aboard ship. Time balls, large black spheres mounted in port in prominent locations,


were dropped at the stroke of noon, enabling any ship in harbor which could see the ball to determine chronometer error. By the end of the U.S. Civil War, telegraph signals were being used to key time balls. Use of radio signals to send time ticks to ships well offshore began in 1904, and soon worldwide signals were available.

109. The Navigational Triangle

Modern celestial navigators reduce their celestial obser- vations by solving a navigational triangle whose points are the elevated pole, the celestial body, and the zenith of the ob- server. The sides of this triangle are the polar distance of the body (codeclination), its zenith distance (coaltitude), and the polar distance of the zenith (colatitude of the observer).

A spherical triangle was first used at sea in solving lunar distance problems. Simultaneous observations were made of the altitudes of the moon and the sun or a star near the ecliptic and the angular distance between the moon and the other body. The zenith of the observer and the two celestial bodies formed the vertices of a triangle whose sides were the two coaltitudes and the angular distance between the bodies. Us- ing a mathematical calculation the navigator “cleared” this distance of the effects of refraction and parallax applicable to each altitude. This corrected value was then used as an argu- ment for entering the almanac. The almanac gave the true lunar distance from the sun and several stars at 3 hour inter- vals. Previously, the navigator had set his watch or checked its error and rate with the local mean time determined by ce- lestial observations. The local mean time of the watch, properly corrected, applied to the Greenwich mean time ob- tained from the lunar distance observation, gave the longitude.

The calculations involved were tedious. Few mariners could solve the triangle until Nathaniel Bowditch published his simplified method in 1802 in The New American Practical Navigator.

Reliable chronometers were available in 1802, but their high cost precluded their general use aboard most ships. However, most navigators could determine their longitude using Bowditch’s method. This eliminated the need for par- allel sailing and the lost time associated with it. Tables for the lunar distance solution were carried in the American nautical almanac until the second decade of the 20th century.

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