《航海学》课程参考文献（地文资料）CHAPTER 03 NAUTICAL CHARTS

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 nauti￾cal 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 le￾gal equivalent of the paper chart when approved by the International Maritime Organization and the various gov￾ernmental agencies which regulate navigation. Currently, however, mariners must maintain a paper chart on the bridge. See Chapter 14, The Integrated Bridge, for a discus￾sion 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 sur￾face is one that can be flattened to form a plane. This process is known as chart projection. If points on the sur￾face 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 car￾tographic principles that apply to paper charts apply to their depiction on video screens. 302. Selecting A Projection Each projection has certain preferable features. How￾ever, as the area covered by the chart becomes smaller, the differences between various projections become less no￾ticeable. On the largest scale chart, such as of a harbor, all projections are practically identical. Some desirable proper￾ties 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 spheri￾cal 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 cyl￾inder tangent along the equator. Similarly, a projection based upon a cylinder tangent along a meridian is called transverse (or inverse) Mercator or transverse (or in￾verse) 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 se￾cant 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 pro￾jection 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 ortho￾graphic 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 equidis￾tant from each other, unlike the terrestrial meridians from which they are derived which converge as the latitude in￾creases. 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 be￾cause 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 longi￾tude lines appears quite different from that described above, since the line of tangency and the equator no longer coin￾cide. 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 in￾clude 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 mea￾sured directly if the spread of latitude is small. Great circles, except meridians and the equator, appear as curved lines con￾cave 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 approxi￾mately the same, while degrees of longitude become progressively shorter. Since degrees of longitude appear ev￾erywhere the same length in the Mercator projection, it is necessary to increase the length of the meridians if the ex￾pansion 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 il￾lustrated in figure 306. The length of a meridian, increased between the equa￾tor 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 pro￾jection. The word “inverse” is used interchangeably with “transverse.” These projections use a fictitious graticule similar to, but offset from, the familiar network of meridi￾ans 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 meridi￾ans, 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 projec￾tion 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 rel￾atively 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 grati￾cule, 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 Washing￾ton 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 rectangu￾lar 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 rectan￾gular coordinates representing declination (ordinate) and sidereal hour angle (abscissa). Since the meridians are par￾allel, 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 cov￾ered to that part of the cone near the surface of the earth limits distortion. A parallel along which there is no distor￾tion 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 (in￾tersecting) 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 sim￾ple 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 be￾comes 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

28NAUTICAL CHARTSthesimpleconic projection isnot perspectivesince onlytheparallels areconcentric circles.Thedistance alonganyme-ridian between consecutiveparallels is in correctrelationtomeridiansareprojectedgeometrically,eachbecominganthe distance on the earth, and, therefore, can be derivedelementofthecone.Whenthisprojection isspreadoutflatmathematically.The pole isrepresented by a circle (Figureto forma map,themeridians appear as straight lines con-312b).The scaleis correct along anymeridian and alongverging attheapex of the cone.The standard parallel.the standard parallel. All other parallels are too great inwhere the cone is tangent to the earth, appears as the arc oflength, with the errorincreasingwith increased distancea circle with its center at the apex of the cone.The otherfromthestandard parallel.Sincethescale isnotthe same inall directions about every point, the projection is neither aconformal norequal-areaprojection.Its non-conformal na-ture is its principal disadvantagefor navigation.Since the scale is correct along the standard paralleland variesuniformlyon eachside,withcomparativelylittledistortion near the standard parallel, this projection is usefulfor mapping an area covering a large spread of longitudeandacomparativelynarrowbandoflatitude.Itwasdevel-oped by Claudius Ptolemy in the second century A.D. tomap just such an area: the Mediterranean Sea.313.LambertConformalProjectionTheuseful latituderangeofthe simpleconicprojectioncan be increased by using a secant cone intersecting theearth at twostandard parallels.SeeFigure313.The area be-tween thetwo standard parallels is compressed, and thatbeyond isexpanded.Suchaprojection is called either a se-cant conic or conic projection with two standardparallels.Figure312a.Asimpleconicprojection.90'E12060°sO'E150'e518090'W150W12OM20WFigure312b.AsimpleconicmapoftheNorthernHemisphere

28 NAUTICAL CHARTS the simple conic projection is not perspective since only the meridians are projected geometrically, each becoming an element of the cone. When this projection is spread out flat to form a map, the meridians appear as straight lines con￾verging at the apex of the cone. The standard parallel, where the cone is tangent to the earth, appears as the arc of a circle with its center at the apex of the cone. The other parallels are concentric circles. The distance along any me￾ridian between consecutive parallels is in correct relation to the distance on the earth, and, therefore, can be derived mathematically. The pole is represented by a circle (Figure 312b). The scale is correct along any meridian and along the standard parallel. All other parallels are too great in length, with the error increasing with increased distance from the standard parallel. Since the scale is not the same in all directions about every point, the projection is neither a conformal nor equal-area projection. Its non-conformal na￾ture is its principal disadvantage for navigation. Since the scale is correct along the standard parallel and varies uniformly on each side, with comparatively little distortion near the standard parallel, this projection is useful for mapping an area covering a large spread of longitude and a comparatively narrow band of latitude. It was devel￾oped by Claudius Ptolemy in the second century A.D. to map just such an area: the Mediterranean Sea. 313. Lambert Conformal Projection The useful latitude range of the simple conic projection can be increased by using a secant cone intersecting the earth at two standard parallels. See Figure 313. The area be￾tween the two standard parallels is compressed, and that beyond is expanded. Such a projection is called either a se￾cant conic or conic projection with two standard Figure 312a. A simple conic projection. parallels. Figure 312b. A simple conic map of the Northern Hemisphere

29NAUTICALCHARTSThepolyconicprojection iswidelyused in atlases,par-ticularly for areas of large range in latitude and reasonablylargerangein longitude,suchas continents.However,sinceit is not conformal, this projection is not customarily usedinnavigation.315.AzimuthalProjectionsIf points on theearthareprojecteddirectlytoaplane sur-face, a map is formed at once, without cutting and flattening,or"developing"This can be considered a special case of a conicprojection in whichthe cone has zero heightThe simplest case of the azimuthal projection is one inwhich the plane is tangent at one ofthepoles.The meridians arestraightlinesintersectingatthepole,andtheparallelsareconcentric circles with their common center at the pole.Theirspacingdepends uponthemethodusedtotransferpointsfromtheearthtotheplaneIf theplane istangent at somepoint other than apolestraight lines through the point oftangency are great circles,and concentriccircleswiththeircommon center atthepointof tangency connect points of equal distance from thatpoint. Distortion, which is zero at the point of tangency, in-Figure313.A secantcone for a conic projection with twocreases along anygreat circle through this point.Along anystandard parallels.circle whose center is the pointof tangency,the distortionis constant.The bearing ofany point from thepoint of tan-If in such a projection the spacing of the parallels is al-gencyiscorrectlyrepresented.It isforthisreasonthatthesetered, suchthatthedistortionisthesamealongthemasprojections are called azimuthal. They are also called ze-nithal Several of the common azimuthal projections arealongthemeridians,theprojectionbecomesconformalThis modification produces theLambert conformal pro-perspective.jection.If the chart is not carried far beyond the standardparallels, and if these are not a great distance apart, the dis-316.GnomonicProjectiontortion over the entire chart is small.A straight line on this projection so nearly approximates aIfaplaneis tangentto theearth,andpoints areprojectedgreat circlethat thetwo are nearlyidentical.Radiobeacon siggeometricallyfrom the center oftheearth, the result is agnonals travel great circles, thus, they can be plotted on thismonic projection. See Figure 316a. Since the projection isprojection without corection.Thisfeature,gained without sac-perspective, it canbe demonstratedbyplacing a light at therificing conformality,has madethis projectionpopularforcenter ofa transparent terrestrial globe and holding aaeronauticalcharts becauseaircraff make wide use ofradioaidsto navigation.Except in highlatitudes,where a slightlymodifiedform ofthis projection has been used for polar charts,it has notreplacedtheMercatorprojectionformarinenavigation.314.Polyconic ProjectionThe latitude limitations of the secant conic projection canbe minimized by using a series of cones. This results in a poly-conic projection.In this projection, each parallel is thebaseofatangentcone.Atthe edgesofthechart, theareabetweenparallels is expanded to eliminate gaps. The scale is correct alongany parallel and along the central meridian of the projectionAlong other meridians the scale increases with increased differ-ence of longitudefrom the central meridian.Parallels appear asnonconcentric circles; meridians appear as curved lines con-Figure316a.An obliquegnomonicprojection.verging toward thepoleand concavetothecentral meridian

NAUTICAL CHARTS 29 If in such a projection the spacing of the parallels is al￾tered, such that the distortion is the same along them as along the meridians, the projection becomes conformal. This modification produces the Lambert conformal pro￾jection. If the chart is not carried far beyond the standard parallels, and if these are not a great distance apart, the dis￾tortion over the entire chart is small. A straight line on this projection so nearly approximates a great circle that the two are nearly identical. Radio beacon sig￾nals travel great circles; thus, they can be plotted on this projection without correction. This feature, gained without sac￾rificing conformality, has made this projection popular for aeronautical charts because aircraft make wide use of radio aids to navigation. Except in high latitudes, where a slightly modified form of this projection has been used for polar charts, it has not replaced the Mercator projection for marine navigation. 314. Polyconic Projection The latitude limitations of the secant conic projection can be minimized by using a series of cones. This results in a poly￾conic projection. In this projection, each parallel is the base of a tangent cone . At the edges of the chart, the area between par￾allels is expanded to eliminate gaps. The scale is correct along any parallel and along the central meridian of the projection. Along other meridians the scale increases with increased differ￾ence of longitude from the central meridian. Parallels appear as nonconcentric circles; meridians appear as curved lines con￾verging toward the pole and concave to the central meridian. The polyconic projection is widely used in atlases, par￾ticularly for areas of large range in latitude and reasonably large range in longitude, such as continents. However, since it is not conformal, this projection is not customarily used in navigation. 315. Azimuthal Projections If points on the earth are projected directly to a plane sur￾face, a map is formed at once, without cutting and flattening, or “developing.” This can be considered a special case of a conic projection in which the cone has zero height. The simplest case of the azimuthal projection is one in which the plane is tangent at one of the poles. The meridians are straight lines intersecting at the pole, and the parallels are con￾centric circles with their common center at the pole. Their spacing depends upon the method used to transfer points from the earth to the plane. If the plane is tangent at some point other than a pole, straight lines through the point of tangency are great circles, and concentric circles with their common center at the point of tangency connect points of equal distance from that point. Distortion, which is zero at the point of tangency, in￾creases along any great circle through this point. Along any circle whose center is the point of tangency, the distortion is constant. The bearing of any point from the point of tan￾gency is correctly represented. It is for this reason that these projections are called azimuthal. They are also called ze￾nithal. Several of the common azimuthal projections are perspective. 316. Gnomonic Projection If a plane is tangent to the earth, and points are projected geometrically from the center of the earth, the result is a gno￾monic projection. See Figure 316a. Since the projection is perspective, it can be demonstrated by placing a light at the center of a transparent terrestrial globe and holding a Figure 313. A secant cone for a conic projection with two standard parallels. Figure 316a. An oblique gnomonic projection

30NAUTICALCHARTSflat surfacetangenttothesphereIn an oblique gnomonic projection the meridians ap-pear as straight lines converging toward the nearer pole.The parallels, except the equator, appear as curves (Figure316b).Asinallazimuthalprojections,bearingsfromtheR8point of tangency are correctly represented.The distancescale, however, changes rapidly,Theprojection is neitherconformal nor equal area.Distortion is so great thatshapesas wellas distances and areas,areverypoorly representedexcept near the pointof tangencyFigure317a.Anequatorial stereographicprojectionFigure 316b.An oblique gnomonic map with point oftangency at latitude30°N, longitude90°W.The usefulness of this projection rests upon the factthat any great circle appears on the map as a straight line,giving charts made on this projection thecommon namegreat-circlechartsGnomonic charts aremostoftenusedforplanningthegreat-circle track between points.Points along thedeter-mined track are then transferred to a Mercator projection.Thegreat circle is thenfollowedbyfollowingtherhumblinesfromonepointtothenext.Computerprogramswhichautomatically calculate great circle routes betweenpointsand providelatitudeandlongitudeofcorresponding rhumblineendpoints arequicklymakingthis use ofthegnomonicchartobsolete.317.StereographicProjectionFigure 317b.A stereographic map of the WesternA stereographic projection results from projectingHemisphere.points on the surfaceoftheearth onto a tangent plane,fromapointonthesurfaceoftheearthoppositethepoint oftan-great circles through the point of tangency appear asgency (Figure 317a). This projection is also called anstraight lines.Other circles such as meridians and parallelsazimuthal orthomorphicprojectionappearas either circles or arcs of circles.The scale of the stereographic projection increasesThe principal navigational use of the stereographicwith distance from the point of tangency, but it increasesprojection is for charts of the polar regions and devices formore slowlythan in the gnomonic projection.The stereo-mechanical or graphical solutionof the navigational trian-graphic projection can showan entire hemispherewithoutgle. A Universal Polar Stereographic (UPS)gridexcessive distortion (Figure317b).As inother azimuthalmathematically adjusted to the graticule, is used as areferprojections,encesystem

30 NAUTICAL CHARTS flat surface tangent to the sphere. In an oblique gnomonic projection the meridians ap￾pear as straight lines converging toward the nearer pole. The parallels, except the equator, appear as curves (Figure 316b). As in all azimuthal projections, bearings from the point of tangency are correctly represented. The distance scale, however, changes rapidly. The projection is neither conformal nor equal area. Distortion is so great that shapes, as well as distances and areas, are very poorly represented, except near the point of tangency. The usefulness of this projection rests upon the fact that any great circle appears on the map as a straight line, giving charts made on this projection the common name great-circle charts. Gnomonic charts are most often used for planning the great-circle track between points. Points along the deter￾mined track are then transferred to a Mercator projection. The great circle is then followed by following the rhumb lines from one point to the next. Computer programs which automatically calculate great circle routes between points and provide latitude and longitude of corresponding rhumb line endpoints are quickly making this use of the gnomonic chart obsolete. 317. Stereographic Projection A stereographic projection results from projecting points on the surface of the earth onto a tangent plane, from a point on the surface of the earth opposite the point of tan￾gency (Figure 317a). This projection is also called an azimuthal orthomorphic projection. The scale of the stereographic projection increases with distance from the point of tangency, but it increases more slowly than in the gnomonic projection. The stereo￾graphic projection can show an entire hemisphere without excessive distortion (Figure 317b). As in other azimuthal projections, great circles through the point of tangency appear as straight lines. Other circles such as meridians and parallels appear as either circles or arcs of circles. The principal navigational use of the stereographic projection is for charts of the polar regions and devices for mechanical or graphical solution of the navigational trian￾gle. A Universal Polar Stereographic (UPS) grid, mathematically adjusted to the graticule, is used as a refer￾ence system. Figure 316b. An oblique gnomonic map with point of tangency at latitude 30°N, longitude 90°W. Figure 317a. An equatorial stereographic projection. Figure 317b. A stereographic map of the Western Hemisphere

31NAUTICALCHARTS318.OrthographicProjectionlines andtheparallels as equally spaced concentriccirclesIf theplane is tangentat somepoint other thana pole,theIfterrestrial points are projected geometrically from in-concentric circles representdistances from the point oftan-finity to a tangent plane, an orthographic projectiongency. In this case, meridians and parallels appear as curves.results(Figure318a).Thisprojection is not conformal; norThe projection can be used to portray the entire earth, thedoes it result in an equal area representation. Its principalpoint 180°from the point oftangency appearing as the largestuse is in navigational astronomy because it is useful for il-of the concentric circles.Theprojection is not conformal,lustrating and solving the navigational triangle.It is alsoequal area,orperspective.Nearthepointoftangencydistor-useful for illustrating celestial coordinates.If the plane istion is small, increasing with distance until shapes near thetangentatapoint on the equator,theparallels(including theopposite side oftheearthare unrecognizable (Figure319)equator)appearas straight lines.Themeridians would apThe projection is useful because it combines the threepear as ellipses, exceptthatthemeridianthroughthepointfeatures ofbeingazimuthal,havingaconstantdistancescaleoftangencywould appearasastraight lineand theone90°fromthepointoftangencyand permitting theentireearthtoaway would appear as a circle (Figure318b).be shownon onemap.Thus, ifan importantharbororairportis selected as thepoint of tangency,thegreat-circle course,distance,and track from thatpointtoany otherpoint on the319.AzimuthalEquidistantProjectionearth arequicklyand accuratelydetermined.For communi-cation work withthe station atthepointoftangency,thepathAn azimuthal equidistant projection is an azimuthalof an incoming signal is at once apparent if the direction ofprojection in which the distance scale along any great circlearrival has been determined and thedirectionto train a direc-through the point of tangency is constant. If a pole is thetional antenna can be determined easily.The projection ispoint of tangency, the meridians appear as straight radialalso usedforpolar charts andforthestar finder,No.2102DFigure318a.Anequatorialorthographicprojection.Figure318b.AnorthographicmapoftheWesternHemisphere

NAUTICAL CHARTS 31 318. Orthographic Projection If terrestrial points are projected geometrically from in￾finity to a tangent plane, an orthographic projection results (Figure 318a). This projection is not conformal; nor does it result in an equal area representation. Its principal use is in navigational astronomy because it is useful for il￾lustrating and solving the navigational triangle. It is also useful for illustrating celestial coordinates. If the plane is tangent at a point on the equator, the parallels (including the equator) appear as straight lines. The meridians would ap￾pear as ellipses, except that the meridian through the point of tangency would appear as a straight line and the one 90° away would appear as a circle (Figure 318b). 319. Azimuthal Equidistant Projection An azimuthal equidistant projection is an azimuthal projection in which the distance scale along any great circle through the point of tangency is constant. If a pole is the point of tangency, the meridians appear as straight radial lines and the parallels as equally spaced concentric circles. If the plane is tangent at some point other than a pole, the concentric circles represent distances from the point of tan￾gency. In this case, meridians and parallels appear as curves. The projection can be used to portray the entire earth, the point 180° from the point of tangency appearing as the largest of the concentric circles. The projection is not conformal, equal area, or perspective. Near the point of tangency distor￾tion is small, increasing with distance until shapes near the opposite side of the earth are unrecognizable (Figure 319). The projection is useful because it combines the three features of being azimuthal, having a constant distance scale from the point of tangency, and permitting the entire earth to be shown on one map. Thus, if an important harbor or airport is selected as the point of tangency, the great-circle course, distance, and track from that point to any other point on the earth are quickly and accurately determined. For communi￾cation work with the station at the point of tangency, the path of an incoming signal is at once apparent if the direction of arrival has been determined and the direction to train a direc￾tional antenna can be determined easily. The projection is also used for polar charts and for the star finder, No. 2102D. Figure 318a. An equatorial orthographic projection. Figure 318b. An orthographic map of the Western Hemisphere

32NAUTICALCHARTS9091008OS0300003000C6060Figure319.An azimuthal equidistant mapof theworld with the point of tangency latitude 40°N, longitude 100°WPOLARCHARTS320.PolarProjectionsthrough a full 3600without stretching or resuming its formerconical shape.Theusefulness ofsuchprojections is also limitedSpecial consideration isgivento the selection of pro-bythefactthat thepole appears as anarc ofacircle instead ofajections forpolarcharts because thefamiliar projectionspoint. However, by using a parallel very near the pole as thebecome special cases with unique features.higher standard parallel,a conic projection with two standardparallels can be made.Thisrequires little stretching to completeIn the case ofcylindrical projections in which the axis ofthethe circles oftheparallels and eliminate that ofthepole.Such acylinder is parallel to the polar axis of the earth, distortion be-projection, called a modified Lambert conformal or Ney'scomesexcessiveandthescalechangesrapidly.Suchprojectionsprojection, is useful for polar charts. It is particularly familiar tocannotbecarried tothepoles.However,boththetransverseandoblique Mercator projections areused.thoseaccustomedtousingtheordinaryLambert conformalcharts in lower latitudes.Conic projections with their axes parallel to the earth's po-laraxisarelimitedintheirusefulnessforpolarchartsbecauseAzimuthal projections areintheir simplestform whenparallels of latitude extending through a full 360° of longitudetangent at a pole.This is because the meridians are straightappear as arcs of circles rather than full circles. This is because alines intersecting at the pole,andparallels are concentriccone,when cut along an elementand flattened, does not extendcircles withtheir commoncenteratthepole.Withinafew

32 NAUTICAL CHARTS POLAR CHARTS 320. Polar Projections Special consideration is given to the selection of pro￾jections for polar charts because the familiar projections become special cases with unique features. In the case of cylindrical projections in which the axis of the cylinder is parallel to the polar axis of the earth, distortion be￾comes excessive and the scale changes rapidly. Such projections cannot be carried to the poles. However, both the transverse and oblique Mercator projections are used. Conic projections with their axes parallel to the earth’s po￾lar axis are limited in their usefulness for polar charts because parallels of latitude extending through a full 360° of longitude appear as arcs of circles rather than full circles. This is because a cone, when cut along an element and flattened, does not extend through a full 360° without stretching or resuming its former conical shape. The usefulness of such projections is also limited by the fact that the pole appears as an arc of a circle instead of a point. However, by using a parallel very near the pole as the higher standard parallel, a conic projection with two standard parallels can be made. This requires little stretching to complete the circles of the parallels and eliminate that of the pole. Such a projection, called a modified Lambert conformal or Ney’s projection, is useful for polar charts. It is particularly familiar to those accustomed to using the ordinary Lambert conformal charts in lower latitudes. Azimuthal projections are in their simplest form when tangent at a pole. This is because the meridians are straight lines intersecting at the pole, and parallels are concentric circles with their common center at the pole. Within a few Figure 319. An azimuthal equidistant map of the world with the point of tangency latitude 40°N, longitude 100°W