CHAPTER 3NAUTICAL CHARTSCHARTFUNDAMENTALS300.Definitions302.SelectingAProjectionEach projection has certain preferablefeatures.How-A nautical chartrepresents part of the spherical earthever,as the area covered by the chart becomes smaller,theon a plane surface.It shows waterdepth, the shoreline ofdifferencesbetweenvariousprojectionsbecomelessnoadjacent land, topographic features, aids to navigation, andticeable.On the largest scale chart, such as of a harbor, allother navigational information. It is a work area on whichprojections arepractically identical.Somedesirable proper-thenavigatorplotscourses,ascertainspositions,andviewsties of a projection are:the relationshipoftheshiptothesurroundingarea.Itassiststhe navigator in avoiding dangers and arriving safely at his1. True shape ofphysical features.destination.2.Correct angular relationship.A projection with thisThe actual form ofa chart mayvary.Traditional nauticharacteristic is conformal ororthomorphiccal charts have been printed on paper.Electronic charts3.Equal area, or the representation of areas in theirconsisting of a digital data base and a display system are incorrectrelativeproportions.use and will eventually replace paper charts for operational4Constant scalevaluesformeasuringdistances.use.An electronic chart is not simplya digital version of aGreat circles represented as straight lines5.paper chart; it introduces a new navigation methodology6.Rhumb linesrepresentedas straight lineswith capabilities and limitations very different from papercharts.The electronic chart will eventually become the le-Some of these properties are mutually exclusive. Forgal equivalent of thepaper chart whenapproved bytheexample,a singleprojection cannotbebothconformalandInternational Maritime Organization and the various gov-equal area. Similarly,both great circles and rhumb linesernmental agencieswhichregulate navigation.Currentlycannot be represented on a single projection as straighthowever,marinersmustmaintainapaper chartonthelines.bridge.See Chapter 14,The Integrated Bridge,for adiscus-sionofelectronic charts.303.Types Of ProjectionsShould a marine accident occur,thenautical chart inThetypeof developablesurfacetowhichthe spheri-use at the time takes on legal significance.In cases ofcal surface is transferred determines the projection'sgrounding,collision,and other accidents,chartsbecomeclassification.Furtherclassificationdependsonwhethercritical records for reconstructing the event and assigningthe projection is centered on the equator (equatorial),aliability.Charts used in reconstructing the incident can alsopole (polar),or somepoint or line between (oblique).Thehavetremendoustrainingvalue.name of a projection indicates its type and its principalfeatures.301.ProjectionsMariners most frequently use a Mercator projection,classified as a cylindrical projection upon a plane, the cyl-Because a cartographer cannot transfer a sphere to ainder tangent along theequator.Similarly,a projectionflat surface withoutdistortion,he must project the surfacebased upon a cylinder tangent along a meridian is calledofasphereontoadevelopablesurface.Adevelopablesur-transverse (or inverse) Mercator or transverse (or in-face is one that can be flattened to form a plane.Thisverse)orthomorphic.TheMercator is themost commonprocess is known as chart projection.If points on the sur-projection used in maritimenavigation,primarily becauseface of the sphere are projected from a single point, therhumb lines plot as straight lines.projection is said to be perspective or geometric.In a simple conic projection,points on the surface ofAs the use of electronic charts becomes increasinglythe earth are transferred to a tangent cone. In the Lambertwidespread, it is important to remember that the same car-conformal projection, the cone intersects the earth (a se-tographic principles that apply to paper charts apply to theircant cone)at two small circles. In a polyconicprojection,depiction on video screens.a series of tangent cones isused.23
23 CHAPTER 3 NAUTICAL CHARTS CHART FUNDAMENTALS 300. Definitions A nautical chart represents part of the spherical earth on a plane surface. It shows water depth, the shoreline of adjacent land, topographic features, aids to navigation, and other navigational information. It is a work area on which the navigator plots courses, ascertains positions, and views the relationship of the ship to the surrounding area. It assists the navigator in avoiding dangers and arriving safely at his destination. The actual form of a chart may vary. Traditional nautical charts have been printed on paper. Electronic charts consisting of a digital data base and a display system are in use and will eventually replace paper charts for operational use. An electronic chart is not simply a digital version of a paper chart; it introduces a new navigation methodology with capabilities and limitations very different from paper charts. The electronic chart will eventually become the legal equivalent of the paper chart when approved by the International Maritime Organization and the various governmental agencies which regulate navigation. Currently, however, mariners must maintain a paper chart on the bridge. See Chapter 14, The Integrated Bridge, for a discussion of electronic charts. Should a marine accident occur, the nautical chart in use at the time takes on legal significance. In cases of grounding, collision, and other accidents, charts become critical records for reconstructing the event and assigning liability. Charts used in reconstructing the incident can also have tremendous training value. 301. Projections Because a cartographer cannot transfer a sphere to a flat surface without distortion, he must project the surface of a sphere onto a developable surface. A developable surface is one that can be flattened to form a plane. This process is known as chart projection. If points on the surface of the sphere are projected from a single point, the projection is said to be perspective or geometric. As the use of electronic charts becomes increasingly widespread, it is important to remember that the same cartographic principles that apply to paper charts apply to their depiction on video screens. 302. Selecting A Projection Each projection has certain preferable features. However, as the area covered by the chart becomes smaller, the differences between various projections become less noticeable. On the largest scale chart, such as of a harbor, all projections are practically identical. Some desirable properties of a projection are: 1. True shape of physical features. 2. Correct angular relationship. A projection with this characteristic is conformal or orthomorphic. 3. Equal area, or the representation of areas in their correct relative proportions. 4. Constant scale values for measuring distances. 5. Great circles represented as straight lines. 6. Rhumb lines represented as straight lines. Some of these properties are mutually exclusive. For example, a single projection cannot be both conformal and equal area. Similarly, both great circles and rhumb lines cannot be represented on a single projection as straight lines. 303. Types Of Projections The type of developable surface to which the spherical surface is transferred determines the projection’s classification. Further classification depends on whether the projection is centered on the equator (equatorial), a pole (polar), or some point or line between (oblique). The name of a projection indicates its type and its principal features. Mariners most frequently use a Mercator projection, classified as a cylindrical projection upon a plane, the cylinder tangent along the equator. Similarly, a projection based upon a cylinder tangent along a meridian is called transverse (or inverse) Mercator or transverse (or inverse) orthomorphic. The Mercator is the most common projection used in maritime navigation, primarily because rhumb lines plot as straight lines. In a simple conic projection, points on the surface of the earth are transferred to a tangent cone. In the Lambert conformal projection, the cone intersects the earth (a secant cone) at two small circles. In a polyconic projection, a series of tangent cones is used
24NAUTICAL CHARTSIn an azimuthal or zenithal projection,points on thecide.These projections are classified as oblique orearth are transferred directly to a plane. If the origin of thetransverse projectionsprojecting rays is the center of the earth, a gnomonic pro-jectionresults,ifitisthepointoppositetheplane'spointoftangency, a stereographic projection, and if at infinity(the projecting lines being parallel to each other),an ortho-graphic projection.The gnomonic, stereographic, andorthographic are perspectiveprojections.In an azimuthalequidistant projection, which is not perspective, the scaleof distances is constant alonganyradial linefromthepointoftangency.SeeFigure303CCFigure303.Azimuthal projections:Agnomonic:Bstereographic;C,(atinfinity)orthographicCylindrical and plane projections are special conicalprojections, using heights infinity and zero, respectivelyAgraticuleisthenetworkoflatitudeandlongitudelines laid out in accordance with the principles of anyprojection.Figure 304. A cylindrical projection.304.Cylindrical Projections305.MercatorProjectionIf a cylinder is placed around the earth,tangent alongNavigatorsmostoftenusetheplaneconformalprojectionthe equator, and the planes of the meridians are extendedknown as the Mercator projection. The Mercator projection isthey intersect the cylinder in a number of vertical lines.Seenot perspective,and its parallels canbederived mathematicallyFigure 304. These parallel lines of projection are equidis-as well as projected geometrically.Its distinguishingfeature istantfromeachother.unliketheterrestrialmeridiansfromthat both the meridians and parallels are expanded at the samewhich they are derived which converge as the latitude in-ratiowith increased latitude.Theexpansion isequal tothesecantcreases. On the earth, parallels oflatitude are perpendicularofthe latitude, with a small correction for the ellipticity of thetothemeridians,forming circles ofprogressivelysmallerearthSincethesecantof9oisinfinity,theprojectioncannotin-diameter as the latitude increases.On the cylinder they arecludethepoles.Sincetheprojection is confomal,expansion isshown perpendicular to the projected meridians, but be-the same in all directions and angles are corectly showncause a cylinder is everywhere of the same diameter, theRhumblinesappearas straightlines,thedirectionsofwhichcanprojected parallels are all the same size.be measured directlyonthechart.Distances can also bemea-If the cylinder is cut along a vertical line (a meridian)sured directly if the spread of latitude is small. Great circles,and spread out flat, the meridians appear as equally spacedexceptmeridians and theequator,appear as curved lines con-vertical lines; and the parallels appear as horizontal linescave to theequator. Small areas appear intheir correct shapebutTheparallels'relativespacingdiffers in thevarioustypes ofofincreased sizeunless theyarenear theequatorcylindrical projections.If the cylinder is tangent along some great circle other306.Meridional Partsthan the equator,theprojected pattern oflatitude and longi-tudelines appearsquitedifferentfromthatdescribed aboveAt the equator a degree of longitude is approximatelysince the line oftangencyand the equator no longer coin-
24 NAUTICAL CHARTS In an azimuthal or zenithal projection, points on the earth are transferred directly to a plane. If the origin of the projecting rays is the center of the earth, a gnomonic projection results; if it is the point opposite the plane’s point of tangency, a stereographic projection; and if at infinity (the projecting lines being parallel to each other), an orthographic projection. The gnomonic, stereographic, and orthographic are perspective projections. In an azimuthal equidistant projection, which is not perspective, the scale of distances is constant along any radial line from the point of tangency. See Figure 303. Cylindrical and plane projections are special conical projections, using heights infinity and zero, respectively. A graticule is the network of latitude and longitude lines laid out in accordance with the principles of any projection. 304. Cylindrical Projections If a cylinder is placed around the earth, tangent along the equator, and the planes of the meridians are extended, they intersect the cylinder in a number of vertical lines. See Figure 304. These parallel lines of projection are equidistant from each other, unlike the terrestrial meridians from which they are derived which converge as the latitude increases. On the earth, parallels of latitude are perpendicular to the meridians, forming circles of progressively smaller diameter as the latitude increases. On the cylinder they are shown perpendicular to the projected meridians, but because a cylinder is everywhere of the same diameter, the projected parallels are all the same size. If the cylinder is cut along a vertical line (a meridian) and spread out flat, the meridians appear as equally spaced vertical lines; and the parallels appear as horizontal lines. The parallels’ relative spacing differs in the various types of cylindrical projections. If the cylinder is tangent along some great circle other than the equator, the projected pattern of latitude and longitude lines appears quite different from that described above, since the line of tangency and the equator no longer coincide. These projections are classified as oblique or transverse projections. 305. Mercator Projection Navigators most often use the plane conformal projection known as the Mercator projection. The Mercator projection is not perspective, and its parallels can be derived mathematically as well as projected geometrically. Its distinguishing feature is that both the meridians and parallels are expanded at the same ratio with increased latitude. The expansion is equal to the secant of the latitude, with a small correction for the ellipticity of the earth. Since the secant of 90° is infinity, the projection cannot include the poles. Since the projection is conformal, expansion is the same in all directions and angles are correctly shown. Rhumb lines appear as straight lines, the directions of which can be measured directly on the chart. Distances can also be measured directly if the spread of latitude is small. Great circles, except meridians and the equator, appear as curved lines concave to the equator. Small areas appear in their correct shape but of increased size unless they are near the equator. 306. Meridional Parts At the equator a degree of longitude is approximately Figure 303. Azimuthal projections: A, gnomonic; B, stereographic; C, (at infinity) orthographic. Figure 304. A cylindrical projection
25NAUTICALCHARTSFigure 306.AMercator map ofthe world.equal in length to a degree oflatitude. As the distancefromwith the cylindertangentalong ameridian,results inathe equator increases, degrees of latitude remain approxi-transverse Mercator or transverse orthomorphic pro-mately the same, while degrees of longitude becomejection.The word“inverse"is used interchangeablywithprogressively shorter. Since degrees oflongitude appear ev-"transverse." These projections use a fictitious graticuleerywhere the same length in the Mercator projection,it issimilar to,but offset from, the familiar network of meridi-necessary to increase the length of the meridians ifthe ex-ans and parallels.The tangent great circle is the fictitiouspansion is tobe equal inall directions.Thus,tomaintaintheequator.Ninety degrees from it are two fictitious poles.Acorrect proportions between degrees oflatitude and degreesgroupofgreatcircles throughthesepoles andperpendicularof longitude,thedegrees of latitude must beprogressivelytothetangentgreatcirclearethefictitiousmeridians.whilelonger as thedistancefromthe equator increases.This is il-a series of circles parallel to the plane of the tangent greatlustrated in figure 306.circleform thefictitious parallels.Theactual meridians andThe length ofa meridian, increased between the equa-parallels appear as curved lines.torandanygivenlatitude,expressed inminutes ofarcattheA straight line on the transverse or oblique Mercatorequatorasaunit,constitutesthenumberofmeridionalpartsprojection makes the same angle with all fictitious meridi-(M) corresponding to that latitude.Meridional parts,givenans, but not with theterrestrial meridians.It is therefore ainTable6foreveryminuteof latitudefromtheequatortofictitious rhumb line.Near the tangent great circle,athepole,make itpossibleto construct a Mercator chartandstraight line closely approximatesagreat circle.Theprojec-tosolveproblems inMercatorsailing.Thesevaluesarefortion is most useful in this area. Since thearea of minimumthe WGS ellipsoid of 1984.distortion is near a meridian,this projection is useful forcharts covering a large band oflatitude and extending a rel-307.Transverse MercatorProjectionsativelyshortdistanceoneachsideofthetangentmeridianIt is sometimesusedforstar chartsshowingtheeveningskyConstructing a chart using Mercator principles, butat various seasons of the year. See Figure 307
NAUTICAL CHARTS 25 equal in length to a degree of latitude. As the distance from the equator increases, degrees of latitude remain approximately the same, while degrees of longitude become progressively shorter. Since degrees of longitude appear everywhere the same length in the Mercator projection, it is necessary to increase the length of the meridians if the expansion is to be equal in all directions. Thus, to maintain the correct proportions between degrees of latitude and degrees of longitude, the degrees of latitude must be progressively longer as the distance from the equator increases. This is illustrated in figure 306. The length of a meridian, increased between the equator and any given latitude, expressed in minutes of arc at the equator as a unit, constitutes the number of meridional parts (M) corresponding to that latitude. Meridional parts, given in Table 6 for every minute of latitude from the equator to the pole, make it possible to construct a Mercator chart and to solve problems in Mercator sailing. These values are for the WGS ellipsoid of 1984. 307. Transverse Mercator Projections Constructing a chart using Mercator principles, but with the cylinder tangent along a meridian, results in a transverse Mercator or transverse orthomorphic projection. The word “inverse” is used interchangeably with “transverse.” These projections use a fictitious graticule similar to, but offset from, the familiar network of meridians and parallels. The tangent great circle is the fictitious equator. Ninety degrees from it are two fictitious poles. A group of great circles through these poles and perpendicular to the tangent great circle are the fictitious meridians, while a series of circles parallel to the plane of the tangent great circle form the fictitious parallels. The actual meridians and parallels appear as curved lines. A straight line on the transverse or oblique Mercator projection makes the same angle with all fictitious meridians, but not with the terrestrial meridians. It is therefore a fictitious rhumb line. Near the tangent great circle, a straight line closely approximates a great circle. The projection is most useful in this area. Since the area of minimum distortion is near a meridian, this projection is useful for charts covering a large band of latitude and extending a relatively short distance on each side of the tangent meridian. It is sometimes used for star charts showing the evening sky at various seasons of the year. See Figure 307. Figure 306. A Mercator map of the world
26NAUTICAL CHARTSFigure309a.AnobliqueMercatorprojection.Figure307.AtransverseMercatormapoftheWesternFictitious PoleHemisphere.308.Universal Transverse Mercator (UTM)GridTrvePoleThe Universal Transverse Mercator (UTM) grid is amilitary grid superimposed upon a transverse Mercator grati-cule, or the representation of these grid lines upon anygraticule. This grid system and these projections are often usedforlarge-scale (harbor)nautical charts and militarycharts.309.ObliqueMercatorProjectionsAMercatorprojection in which thecylinderistangentalong a great circle other than the equator or a meridian iscalled an oblique Mercator or oblique orthomorphicprojection.This projection is used principally to depict anarea in the nearvicinityof an oblique great circle.Figure309c,forexample,showsthegreatcircle joiningWashington andMoscow.Figure309d shows an obliqueMercatormap with the great circle between these two centers as thetangent great circle or fictitious equator.The limits of thechartof Figure309c are indicated inFigure309d.Note theFigure 309b.The fictitious graticle of an obliquelargevariation in scaleas the latitudechanges.Mercatorprojection
26 NAUTICAL CHARTS 308. Universal Transverse Mercator (UTM) Grid The Universal Transverse Mercator (UTM) grid is a military grid superimposed upon a transverse Mercator graticule, or the representation of these grid lines upon any graticule. This grid system and these projections are often used for large-scale (harbor) nautical charts and military charts. 309. Oblique Mercator Projections A Mercator projection in which the cylinder is tangent along a great circle other than the equator or a meridian is called an oblique Mercator or oblique orthomorphic projection. This projection is used principally to depict an area in the near vicinity of an oblique great circle. Figure 309c, for example, shows the great circle joining Washington and Moscow. Figure 309d shows an oblique Mercator map with the great circle between these two centers as the tangent great circle or fictitious equator. The limits of the chart of Figure 309c are indicated in Figure 309d. Note the large variation in scale as the latitude changes. Figure 307. A transverse Mercator map of the Western Hemisphere. Figure 309a. An oblique Mercator projection. Figure 309b. The fictitious graticle of an oblique Mercator projection
27NAUTICAL CHARTSFFigure309c.Thegreat circlebetweenWashingtonandMoscowas itappears ona Mercatormap.Figure309d.An obliqueMercatormapbased upon a cylindertangentalongthegreat circlethroughWashington andMoscow.Themap includes an area 500milesoneach sideof thegreatcircle.Thelimits of thismapare indicated on theMercatormapofFigure309c310.RectangularProjectionconverging toward thenearerpole.Limiting the area cov-ered to that part of the cone near the surface of the earthlimits distortion.Aparallel along which there is no distor-Acylindrical projection similarto theMercator,buttion is called a standard parallel. Neither the transversewith uniform spacing of the parallels, is called a rectangu-conic projection, in which the axis of the cone is in thelar projection.It is convenient for graphically depictingequatorialplane,northeobliqueconicprojection,inwhichinformationwheredistortion is not important.Theprincipalthe axis ofthe cone is oblique to the plane oftheequator,isnavigationaluseofthisprojection isforthestarchartoftheordinarily used for navigation. They are typically used forAirAlmanac,wherepositionsofstars areplottedbyrectan-illustrativemaps.gular coordinates representing declination (ordinate) andsidereal hour angle(abscissa).Sincethe meridians are par-Using cones tangent at various parallels, a secant (in-allel,theparallels of latitude (including the equator and thetersecting)cone,or a series of cones varies the appearancepoles)areall representedbylinesofequal length.andfeaturesofaconicprojection.31l1.ConicProjections312.SimpleConicProjectionA conicprojectionis producedbytransferringpointsA conicprojectionusingasingle tangent cone isa sim-from the surface ofthe earthtoa cone or series of cones.ple conic projection (Figure 312a).The height of the coneThis cone is then cut along an element and spread outflat toincreases as the latitudeofthetangent parallel decreases.Atform the chart.When the axis ofthe cone coincides with thethe equator, the height reaches infinity and the cone be-axis of the earth, then theparallelsappear as arcs ofcircles,comesacvlinder.Atthepole,itsheightiszero,andtheand themeridians appearaseither straight or curved linescone becomes aplane.Similarto the Mercatorprojection
NAUTICAL CHARTS 27 310. Rectangular Projection A cylindrical projection similar to the Mercator, but with uniform spacing of the parallels, is called a rectangular projection. It is convenient for graphically depicting information where distortion is not important. The principal navigational use of this projection is for the star chart of the Air Almanac, where positions of stars are plotted by rectangular coordinates representing declination (ordinate) and sidereal hour angle (abscissa). Since the meridians are parallel, the parallels of latitude (including the equator and the poles) are all represented by lines of equal length. 311. Conic Projections A conic projection is produced by transferring points from the surface of the earth to a cone or series of cones. This cone is then cut along an element and spread out flat to form the chart. When the axis of the cone coincides with the axis of the earth, then the parallels appear as arcs of circles, and the meridians appear as either straight or curved lines converging toward the nearer pole. Limiting the area covered to that part of the cone near the surface of the earth limits distortion. A parallel along which there is no distortion is called a standard parallel. Neither the transverse conic projection, in which the axis of the cone is in the equatorial plane, nor the oblique conic projection, in which the axis of the cone is oblique to the plane of the equator, is ordinarily used for navigation. They are typically used for illustrative maps. Using cones tangent at various parallels, a secant (intersecting) cone, or a series of cones varies the appearance and features of a conic projection. 312. Simple Conic Projection A conic projection using a single tangent cone is a simple conic projection (Figure 312a). The height of the cone increases as the latitude of the tangent parallel decreases. At the equator, the height reaches infinity and the cone becomes a cylinder. At the pole, its height is zero, and the cone becomes a plane. Similar to the Mercator projection, Figure 309c. The great circle between Washington and Moscow as it appears on a Mercator map. Figure 309d. An oblique Mercator map based upon a cylinder tangent along the great circle through Washington and Moscow. The map includes an area 500 miles on each side of the great circle. The limits of this map are indicated on the Mercator map of Figure 309c