Chapt-03.pdf

CHAPTER 3

NAUTICAL CHARTS

CHART FUNDAMENTALS

300. Definitions

302. Selecting a Projection

A nautical chart represents part of the spherical earth

on a plane surface. It shows water depth, the shoreline of

adjacent land, prominent topographic features, aids to nav-

igation, and other navigational information. It is a work

area on which the navigator plots courses, ascertains posi-

tions, and views the relationship of the ship to the

surrounding area. It assists the navigator in avoiding dan-

gers and arriving safely at his destination.

Originally hand-drawn on sheepskin, traditional nauti-

cal charts have for generations been printed on paper.

Electronic charts consisting of a digital data base and a

display system are in use and are replacing paper charts

aboard many vessels. An electronic chart is not simply a

digital version of a paper chart; it introduces a new naviga-

tion methodology with capabilities and limitations very

different from paper charts. The electronic chart is the legal

equivalent of the paper chart if it meets certain International

Maritime Organization specifications. See Chapter 14 for a

complete 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.

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 relationships

3. Equal area (Represents areas in proper proportions)

4. Constant scale values

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 can-

not 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 classifica-

tion. 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.

In an azimuthal or zenithal projection , points on the

earth are transferred directly to a plane. If the origin of the

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.

NAUTICAL CHARTS

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 .Inan 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.

Figure 303. Azimuthal projections: A, gnomonic; B,

stereographic; C, (at infinity) orthographic.

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.

Figure 304. A cylindrical projection.

304. Cylindrical Projections

305. Mercator Projection

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 .

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

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

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

NAUTICAL CHARTS

Figure 306. A Mercator map of the world.

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 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.

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 merid-

ians, 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 pro-

jection 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 ex-

tending 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.

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-

NAUTICAL CHARTS

as the latitude changes.

Figure 309a. An oblique Mercator projection.

Figure 307. A transverse Mercator map of the Western

Hemisphere.

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 . See Figure 309a and Figure 309b . This projec-

tion 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 fic-

titious equator. The limits of the chart of Figure 309c are

indicated in Figure 309d . Note the large variation in scale

Figure 309b. The fictitious graticule of an oblique

Mercator projection.

NAUTICAL CHARTS

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 .

310. Rectangular Projection

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.

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

312. Simple Conic Projection

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,

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-

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