Maps and Charts

Aviators use air navigation to determine where they are going and how to get there. This category serves as a reference for techniques and methods used in air navigation.

In addition to this section, several other sources provide excellent references to methods and techniques of navigation:

• The Journal of the Institute of Navigation—published quarterly by The Institute of Navigation, 1800 Diagonal Road, Alexandria, Virginia, 22314, and covers the latest in navigation technology.
• The United States Observatory and United States Navy Oceanographic Office—publications include the Air Almanac, Nautical Almanac, NV Publication 9 (Volumes 1 and 2).
• The American Practical Navigator, SR Publication 249, Volumes 1 through 3, Sight Reduction Tables for Air Navigation and Catalog, and the NGA Public Sale Aeronautical Charts and Products—published by the National Geo-Spatial Intelligence Agency (NGA) (formally known as the National Imagery and Mapping Agency (NIMA)).
• Dutton’s Navigation and Piloting—published by the Naval Institute Press, Annapolis, Maryland.

Basic Terms

Basic to the study of navigation is an understanding of certain terms that could be called the dimensions of navigation. The navigator uses these dimensions of position, direction, distance, altitude, and time as basic references.

A clear understanding of these dimensions as they relate to navigation is necessary to provide the navigator with a means of expressing and accomplishing the practical aspects of air navigation. These terms are defined as follows:

• Position—a point defined by stated or implied coordinates. Though frequently qualified by such adjectives as estimated, dead reckoning (DR), no wind, and so forth, the word position always refers to some place that can be identified. It is obvious that a navigator must know the aircraft’s current position before being able to direct the aircraft to another position or in another direction.
• Direction—the position of one point in space relative to another without reference to the distance between them. Direction is not in itself an angle, but it is often measured in terms of its angular distance from a referenced direction.
• Distance—the spatial separation between two points, measured by the length of a line joining them. On a plane surface, this is a simple problem. However, consider distance on a sphere, where the separation between points may be expressed as a variety of curves. It is essential that the navigator decide exactly how the distance is to be measured. The length of the line can be expressed in various units (e.g., nautical miles (NM) or yards).
• Altitude—the height of an aircraft above a reference plane. Altitude can be measured as absolute or pressure. Absolute altitude is measured by a radar altimeter, and pressure altitude is measured from various datum planes. Compare with elevation, which is the height of a point or feature on the earth above a reference plane.
• Time—defined in many ways, but definitions used in navigation consist mainly of:
  1. Hour of the day.
  2. Elapsed interval.
• Methods of expression—the methods of expressing position, direction, distance, altitude, and time are covered fully in the appropriate categories within this section. These terms, and others similar to them, represent definite quantities or conditions that may be measured in several different ways. For example, the position of an aircraft may be expressed in coordinates, such as a certain latitude and longitude. The position may also be expressed as 10 miles south of a certain city. The study of navigation demands the navigator learn how to measure quantities, such as those just defined and how to apply the units by which they are expressed.

The Earth (Part One)

Shape and Size

For most navigational purposes, the earth is assumed to be a perfect sphere, although in reality it is not. Inspection of the earth’s crust reveals there is a height variation of approximately 12 miles from the top of the tallest mountain to the bottom of the deepest point in the ocean. A more significant deviation from round is caused by a combination of the earth’s rotation and its structural flexibility. When taking the ellipsoidal shape of the planet into account, mountains seem rather insignificant. The peaks of the Andes are much farther from the center of the earth than Mount Everest.

Measured at the equator, the earth is approximately 6,378,137 meters in diameter, while the polar diameter is approximately 6,356,752.3142 meters. The difference in these diameters is 21,384.6858 meters, and this difference may be used to express the ellipticity of the earth. The ratio between this difference and the equatorial diameter is:

Since the equatorial diameter exceeds the polar diameter by only 1 part in 298, the earth is nearly spherical. A symmetrical body having the same dimensions as the earth, but with a smooth surface, is called an ellipsoid. The ellipsoid is sometimes described as a spheroid, or an oblate spheroid.

In Figure 1-1, polar north (Pn), east (E), polar south (Ps), and west (W) represent the surface of the earth. Pn and Ps represent the axis of rotation. The earth rotates from west to east. All points in the hemisphere Pn, W, Ps approach the reader, while those in the opposite hemisphere recede from the reader. The circumference W-E is called the equator, which is defined as that imaginary circle on the surface of the earth whose plane passes through the center of the earth and is perpendicular to the axis of rotation.

Figure 1-1. Schematic representation of the earth showing its axis of rotation and equator.

Great Circles and Small Circles

A great circle is defined as a circle on the surface of a sphere whose center and radius are those of the sphere itself. It is the largest circle that can be drawn on the sphere; it is the intersection with the surface of the earth of any plane passing through the earth’s center. The arc of a great circle is the shortest distance between two points on a sphere, just as a straight line is the shortest distance between two points on a plane. On any sphere, an indefinitely large number of great circles may be drawn through any point, though only one great circle may be drawn through any two points not diametrically opposite. Several great circles are shown in Figure 1-2.

Figure 1-2. A great circle is the largest circle in a sphere.

Circles on the surface of the sphere, other than great circles, may be defined as small circles. A small circle is a circle on the surface of the earth whose center and/or radius are not that of the sphere. A set of small circles, called latitude, is discussed later. In summary, the intersection of a sphere and a plane is a great circle if the plane passes through the center of the sphere and a small circle if it does not.

Latitude and Longitude

The nature of a sphere is such that any point on it is exactly like any other point. There is neither beginning nor ending as far as differentiation of points is concerned. In order that points may be located on the earth, some points or lines of reference are necessary so that other points may be located with regard to them. The location of New York City with reference to Washington, D.C. can be stated as a number of miles in a certain direction from Washington. Any point on the earth can be located in this manner.

Imaginary Reference Lines

Such a system, however, does not lend itself readily to navigation, because it would be difficult to locate a point precisely in mid-ocean without any nearby geographic features to use for reference. We use a system of coordinates to locate positions on the earth by means of imaginary reference lines. These lines are known as parallels of latitude and meridians of longitude.

Latitude

Once a day, the earth rotates on its north-south axis, which is terminated by the two poles. The equatorial plane is constructed at the midpoint of this axis at right angles to it. [Figure 1-3] A great circle drawn through the poles is called a meridian, and an infinite number of great circles may be constructed in this manner. Each meridian is divided into four quadrants by the equator and the poles. The circle is arbitrarily divided into 360°, and each of these quadrants contains 90°.

Figure 1-3. Planes of the earth.

Take a point on one of these meridians 30° N of the equator. Through this point passes a plane perpendicular to the northsouth axis of rotation. This plane is parallel to the plane of the equator as shown in Figure 1-3 and intersects the earth in a small circle called a parallel or parallel of latitude. The particular parallel of latitude chosen as 30° N, and every point on this parallel is at 30° N. In the same way, other parallels can be constructed at any desired latitude, such as 10°, 40°, etc.

Bear in mind that the equator is drawn as the great circle; midway between the poles and parallels of latitude are small circles constructed with reference to the equator. The angular distance measured on a meridian north or south of the equator is known as latitude [Figure 1-4] and forms one component of the coordinate system.

Figure 1-4. Latitude as an angular measurement.

The Earth (Part Two)

Longitude

The latitude of a point can be shown as 20° N or 20° S of the equator, but there is no way of knowing whether one point is east or west of another. This difficulty is resolved by use of the other component of the coordinate system, longitude, which is the measurement of this east-west distance. Longitude, unlike latitude, has no natural starting point for numbering. The solution has been to select an arbitrary starting point.

A great many places have been used, but when the Englishspeaking people began to make charts, they chose the meridian through their principal observatory in Greenwich, England, as the origin for counting longitude. This Greenwich meridian is sometimes called the prime meridian, though actually it is the zero meridian. Longitude is counted east and west from this meridian through 180°. [Figure 1-5] Thus, the Greenwich meridian is the 0° longitude on one side of the earth and, after crossing the poles, it becomes the 180th meridian (180° east or west of the 0° meridian).

Figure 1-5. Longitude is measured east and west of the Greenwich Meridian.

In summary, if a globe has the circles of latitude and longitude drawn upon it according to the principles described, any point can be located on the globe using these measurements. [Figure 1-6]

Figure 1-6. Latitude is measured from the equator; longitude from the prime meridian.

It is beneficial to point out here some of the measurements used in the coordinate system. Latitude is measured in degrees up to 90, and longitude is expressed in degrees up to 180. The total number of degrees in any one circle is always 360. A degree (°) of arc may be subdivided into smaller units by dividing each degree into 60 minutes (‘) of arc. Each minute may be further subdivided into 60 seconds (“) of arc.

Measurement may also be expressed in degrees, minutes, and tenths of minutes.

A position on the surface of the earth is expressed in terms of latitude and longitude. Latitude is expressed as being either north or south of the equator, and longitude as either east or west of the prime meridian.

In actual practice, map production requires surveyors to measure the latitude and longitude of geographic objects in their area of interest. Local variation in the earth’s gravity field can cause these measurements to be inconsistent. All coordinates from maps, charts, traditional surveys, and satellite positioning systems are tied to an individual mathematical model of the earth called a datum. Coordinates for a given point may differ between datums by hundreds of yards. In other words, latitude and longitude measured directly from observation of stars (called an astronomic coordinate) is consistent, but it may not match maps, charts, or surveyed points. The theoretical consistency of latitude and longitude is therefore not achievable in reality. Without knowledge of the datum used to establish a particular map or surveyed coordinate, the coordinate is suspect at best.

Distance

Distance, as previously defined, is measured by the length of a line joining two points. The standard unit of distance for navigation is the nautical mile (NM). The NM can be defined as either 6,076 feet or 1 minute of latitude. Sometimes it is necessary to convert statute miles (SM) to NM and vice versa. This conversion is easily done with the following ratio:

Closely related to the concept of distance is speed, which determines the rate of change of position. Speed is usually expressed in miles per hour (mph), this being either SM per hour or NM per hour. If the measure of distance is NM, it is customary to speak of speed in terms of knots. Thus, a speed of 200 knots and a speed of 200 NM per hour are the same thing. It is incorrect to say 200 knots per hour unless referring to acceleration.

Direction

Remember, direction is the position of one point in space relative to another without reference to the distance between them. The time honored point system for specifying a direction as north, north-northwest, northwest, westnorthwest, west, etc., is not adequate for modern navigation. It has been replaced for most purposes by a numerical system. [Figure 1-7] The numerical system divides the horizon into 360°, starting with north as 000° and continuing clockwise through east 090°, south 180°, west 270°, and back to north.

Figure 1-7. Numerical system is used in air navigation.

The circle, called a compass rose, represents the horizon divided into 360°. The nearly vertical lines in Figure 1-7 are meridians drawn as straight lines with the meridian of position A passing through 000° and 180° of the compass rose. Position B lies at a true direction of 062° from A, and position C is at a true direction of 220° from A.

Since determination of direction is one of the most important parts of the navigator’s work, the various terms involved should be clearly understood. Generally, in navigation, unless otherwise stated, directions are called true directions.

Course

Course is the intended horizontal direction of travel. Heading is the horizontal direction in which an aircraft is pointed. Heading is the actual orientation of the longitudinal axis of the aircraft at any instant, while course is the direction intended to be made good. Track is the actual horizontal direction made by the aircraft over the earth.

Bearing

Bearing is the horizontal direction of one terrestrial point from another. As illustrated in Figure 1-8, the direction of the island from the aircraft is marked by a visual bearing called the line of sight (LOS). Bearings are usually expressed in terms of one of two reference directions: true north (TN) or the direction in which the aircraft is pointed. If TN is the reference direction, the bearing is called a true bearing (TB). If the reference direction is the heading of the aircraft, the bearing is called a relative bearing (RB). [Figure 1-9]

Figure 1-8. Measuring true bearing from true north.Figure 1-9. Measuring relative bearing from aircraft heading.

Great Circle and Rhumb Line Direction

The direction of the great circle, shown in Figure 1-10, makes an angle of about 40° with the meridian near Washington, D.C., about 85° with the meridian near Iceland, and a still greater angle with the meridian near Moscow. In other words, the direction of the great circle is constantly changing as progress is made along the route and is different at every point along the great circle. Flying such a route requires constant change of direction and would be difficult to fly under ordinary conditions. Still, it is the most desirable route because it is the shortest distance between any two points.

Figure 1-10. Great circle.

A line that makes the same angle with each meridian is called a rhumb line. An aircraft holding a constant true heading would be flying a rhumb line. Flying this sort of path results in a greater distance traveled, but it is easier to steer. If continued, a rhumb line spirals toward the poles in a constant true direction but never reaches them. The spiral formed is called a loxodrome or loxodromic curve. [Figure 1-11]

Figure 1-11. A rhumb line or loxodrome.

Between two points on the earth, the great circle is shorter than the rhumb line, but the difference is negligible for short distances (except in high latitudes) or if the line approximates a meridian or the equator.

Understanding Time in Celestial Navigation

In celestial navigation, navigators determine the aircraft’s position by observing the celestial bodies. The apparent position of these bodies changes with time. Therefore, determining the aircraft’s position relies on timing the observation exactly. Time is measured by the rotation of the earth and the resulting apparent motions of the celestial bodies.

This category considers several different systems of measurement, each with a special use. Before learning the various kinds of time, it is important to understand transit. Notice in Figure 1-12 that the poles divide the observer’s meridian into halves. The observer’s position is in the upper branch. The lower branch is the opposite half. Every day, because of the earth’s rotation, every celestial body transits the upper and lower branches of the observer’s meridian. The first kind of time presented here is solar time.

Figure 1-12. Transit is caused by the earth’s rotation.

Apparent Solar Time

The sun as it is seen in the sky is called the true sun or the apparent sun. Apparent solar time is based upon the movement of the sun as it crosses the sky. A sundial accurately indicates apparent solar time. Apparent solar time is not useful, because the apparent length of day varies throughout the year. A timepiece would have to operate at different speeds to indicate correct apparent time. However, apparent time accurately indicates upper and lower transit. Upper transit occurs at noon; apparent time and lower transit at midnight apparent time. Difficulties in using apparent time led to the introduction of mean time.

Mean Solar Time

A mean day is an artificial unit of constant length, based on the average of all apparent solar days over a period of years. Time for a mean day is measured with reference to a fictitious body, the mean sun, so designed that its hour circle moves westward at a constant rate along the celestial equator. Time computed using the mean sun is called mean solar time. The coordinates of celestial bodies in the Air Almanac are tabulated in mean solar time, making it the time of primary interest to navigators. The difference in length between the apparent day (based upon the true sun) and the mean day (based upon the mean sun) is never as much as a minute. The differences are cumulative, however, so that the imaginary mean sun precedes or follows the apparent sun by approximately 15 minutes at certain times during the year.

Greenwich Mean Time (GMT)

Greenwich Mean Time (GMT) is used for most celestial computations. GMT is mean solar time measured from the lower branch of the Greenwich meridian westward through 360° to the upper branch of the hour circle passing through the mean sun. [Figure 1-13] The mean sun transits the Greenwich meridian’s lower branch at GMT 2400 (0000) each day and the upper branch at GMT 1200. The meridian at Greenwich is the logical selection for this reference, as it is the origin for the measurement of Greenwich hour angle (GHA) and the reckoning of longitude. Consequently, celestial coordinates and other information are tabulated in almanacs with reference to GMT. GMT is also called Zulu or Z time.

Figure 1-13. Measuring Greenwich mean time.

Local Mean Time (LMT)

Just as GMT is mean solar time measured with reference to the Greenwich meridian, local mean time (LMT) is mean solar time measured with reference to the observer’s meridian. LMT is measured from the lower branch of the observers meridian, westward through 360°, to the upper branch of the hour circle passing through the mean sun. [Figure 1-13] The mean sun transits the lower branch of the observer’s meridian at LMT 0000 (2400) and the upper branch at LMT 1200. For an observer at the Greenwich meridian, GMT is LMT. Navigators use LMT to compute local sunrise, sunset, twilight, moonrise, and moonset at various latitudes along a given meridian.

Relationship of Time and Longitude

The mean sun travels at a constant rate, covering 360° of arc in 24 hours. The mean sun transits the same meridian twice in 24 hours. The following relationships exists between time and arc:

Time	Arc
24 hours	360°
1 hour	15°
4 minutes	1°
1 minute	15′

Local time is the time at one particular meridian. Since the sun cannot transit two meridians simultaneously, no two meridians have exactly the same local time. The difference in time between two meridians is the time of the sun’s passage from one meridian to the other. This time is proportional to the angular distance between the two meridians. One hour is equivalent to 15°.

If two meridians are 30° apart, their time differs by 2 hours. The easternmost meridian has a later local time, because the sun has crossed its lower branch first; thus, the day is older there. These statements hold true whether referring to the apparent sun or the mean sun. Figure 1-14 demonstrates that the sun crossed the lower branch of the meridian of observer 1 at 60° east longitude 4 hours before it crossed the lower branch of the Greenwich meridian (60 ÷ 15) and 6 hours before it crossed the lower branch of the meridian of observer 2 at 30° west longitude (90 ÷ 15). Therefore, the local time at 60° east longitude is later by the respective amounts.

Figure 1-14. Local time differences at different longitudes.

Standard Time Zone

The world is divided into 24 zones, each zone being 15° of longitude wide. Each zone uses the LMT of its central meridian. (A few areas of the world are further divided and use half-hour increments from GMT. Some notable examples include India, Bangladesh, Newfoundland, and parts of Australia and Thailand.) Since the Greenwich meridian is the central meridian for one of the zones, and each zone is 15° or 1 hour wide, the time in each zone differs from GMT by an integral number of hours. The zones are designated by numbers from 0 to 12 and –12, each indicating the number of hours that must be added or subtracted to local zone time (LZT) to obtain GMT. Since the time is earlier in the zones west of Greenwich, the numbers of these zones are plus; in those zones east of Greenwich, the numbers are minus. [Figure 1-15] Ground forces frequently refer to the zones by letters of the alphabet, and air forces use one of these letters (Z) for GMT. The zone boundaries have been modified to conform with geographical boundaries for greater convenience. For example, in case a zone boundary passed through a city, it would be impractical to use the time of one zone in one part of the city and the time of the adjacent zone in the other part. In some countries, which overlap two or three zones, one time is used throughout.

Figure 1-15. Standard time zones.

Date Changes at Midnight

If travelling west from Greenwich around the world and setting a watch back an hour for each time zone, the watch would have been set back a total of 24 hours on arriving back at Greenwich, and the date would be 1 day behind. Conversely, traveling eastward, the watch would have been advanced a total of 24 hours, gaining a day.

To keep straight, a day must be added somewhere if going around the world to the west and a day must be lost if going around to the east. The 180° meridian is the international dateline where a day is gained or lost. The date line follows the meridian except where it detours to avoid eastern Siberia, the western Aleutian Islands, and several groups of islands in the South Pacific.

The local civil date changes at 2400 or midnight. Thus, the date changes as the mean sun transits the lower branch of the meridian. Consider the situation in another way. The hour circle of the mean sun is divided in half at the poles. On the half away from the sun (the lower branch), it is always midnight LMT. As the lower branch moves westward, it pushes the old date before it and drags the new date after it. [Figure 1-16] As the lower branch approaches the 180° meridian, the area of the old date decreases and the area of the new date increases. When the lower branch reaches the date line; that is, when the mean sun transits the Greenwich meridian, the old date is crowded out and the new date for that instant prevails in the world. Then, as the lower branch passes the date line, a newer date begins east of the lower branch and the process starts all over again. The zone date changes at midnight zone time (ZT) or when the lower branch of the mean sun transits the central meridian of the zone.

Figure 1-16. Zone date changes. [click image to enlarge]

Time Conversion

Sometimes it is necessary to convert LMT time to GMT, or GMT to LMT. The Air Almanac contains a table for conversion of arc to time at a rate of 15° of arc per hour of time. [Figure 1-17] This conversion is only good for LMT to GMT, or GMT to LMT. ZT is influenced by daylight savings time and geographical boundaries. For example, to convert GMT to LMT at 126° –36′ W:

126° 00 = 8 h 24 min 00s
36′ = 02 min 24s
126° 36′ = 8 h 26 min 24s

To derive LMT from GMT, subtract the time in the Western Hemisphere and add it in the Eastern Hemisphere. Do the opposite to convert LMT to GMT.

Figure 1-17. Air almanac conversion of arc to time. [click image to enlarge]

Sidereal Time

Solar time is measured with reference to the true sun or the mean sun. Time may also be measured relative to a fixed point in space. Time measured with reference to the first point of Aries, which is considered stationary although it moves slightly, is sidereal or star time. The first point of Aries is defined as where the sun crosses the equator northbound on the first day of spring.

The sidereal day begins when the first point of Aries transits the upper branch of the observer’s meridian. Local sidereal time (LST) is the number of hours that the first point of Aries has moved westward from the observers meridian. Expressed in degrees, it equals the local hour angle (LHA) of Aries. [Figure 1-18] LST at Greenwich is Greenwich sidereal time (GST), which is equivalent to the GHA of Aries. GST, or GHA of Aries, specifies the position of the stars with relation to the earth. Thus, a given star is in the same position relative to the earth at the same sidereal time each day.

Figure 1-18. Greenwich sidereal time.

Number of Days in a Year

The earth revolves around the sun in a year. The number of days in the year equals the number of rotations of the earth during one revolution. The earth rotates eastward about 366.24 times during its yearly eastward revolution. The total effect of one revolution and 366.24 rotations is that the sun appears to revolve around the earth 365.24 times per year. Therefore, there are 365.24 solar days per year. Since the sidereal day is measured with reference to a fixed point, the length of the sidereal day is the period of the earth’s rotation. Therefore, the number of sidereal days in the year is equal to the number of rotations per year, 366.24.

Navigator’s Use of Time

Navigators use three different kinds of time: GMT, LMT, and ZT. All three are based upon the motions of the fictitious mean sun. The mean sun revolves about the earth at the average rate of the apparent sun, completing one revolution in 24 hours. Time is based upon the motion of the sun relative to a given meridian. The time is 2400/0000 at lower transit and 1200 at upper transit. In GMT, the reference meridian is that of Greenwich; in LMT, the reference meridian is that of a given place; in ZT, the reference meridian is the standard meridian of a given zone.

The difference between two times equals the difference of longitude of their reference meridians expressed in time. GMT differs from ZT by the longitude of the zone’s standard meridian; LMT differs from ZT by the difference of longitude between the zone’s standard meridian and the meridian of the place. In interconverting ZT and GMT, the navigator uses the zone description. The zone difference is the time difference between its standard meridian and GMT, and it has a sign to indicate the correction to ZT to obtain GMT. The sign is plus (+) for west longitude and minus (–) for east longitude.

Charts and Projections (Part One)

There are several basic terms and ideas relative to charts and projections that the reader should be familiar with before discussing the various projections used in the creation of aeronautical charts.

1. A map or chart is a small scale representation on a plane of the surface of the earth or some portion of it.
2. The chart projection forms the basic structure on which a chart is built and determines the fundamental characteristics of the finished chart.
3. There are many difficulties that must be resolved when representing a portion of the surface of a sphere upon a plane. Two of these are distortion and perspective.

• Distortion cannot be entirely avoided, but it can be controlled and systematized to some extent in the drawing of a chart. If a chart is drawn for a particular purpose, it can be drawn in such a way as to minimize the type of distortion that is most detrimental to the purpose. Surfaces that can be spread out in a plane without stretching or tearing, such as a cone or cylinder, are called developable surfaces, and those like the sphere or spheroid that cannot be formed into a plane without distortion are called non-developable. [Figure 1-19] The problem of creating a projection lies in developing a method for transferring the meridians and parallels to the chart in a manner that preserves certain desired characteristics as nearly as possible. The methods of projection are either mathematical or perspective.

Figure 1-19. Developable and nondevelopable surfaces.

• The perspective or geometric projection consists of projecting a coordinate system based on the earth-sphere from a given point directly onto a developable surface. The properties and appearance of the resultant map depends upon two factors: the type of developable surface and the position of the point of projection.

2. The mathematical projection is derived analytically to provide certain properties or characteristics that cannot be arrived at geometrically. Consider some of the choices available for selecting projections that best accommodate these properties and characteristics.

Choice of Projection

The ideal chart projection would portray the features of the earth in their true relationship to each other; that is, directions would be true and distances would be represented at a constant scale over the entire chart. This would result in equality of area and true shape throughout the chart. Such a relationship can only be represented on a globe. On a flat chart, it is impossible to preserve constant scale and true direction in all directions at all points, nor can both relative size and shape of the geographic features be accurately portrayed throughout the chart. The characteristics most commonly desired in a chart projection are conformality, constant scale, great circles as straight lines, rhumb lines as straight lines, true azimuth, and geographic position easily located.

Conformality

Conformality is very important for air navigation charts. For any projection to be conformal, the scale at any point must be independent of azimuth. This does not imply, however, that the scales at two points at different latitudes are equal. It means the scale at any given point is, for a short distance, equal in all directions. For conformality, the outline of areas on the chart must conform in shape to the feature being portrayed. This condition applies only to small and relatively small areas; large land masses must necessarily reflect any distortion inherent in the projection. Finally, since the meridians and parallels of earth intersect at right angles, the longitude and latitude lines on all conformal projections must exhibit this same perpendicularity. This characteristic facilitates the plotting of points by geographic coordinates.

Constant Scale

The property of constant scale throughout the entire chart is highly desirable, but impossible to obtain as it would require the scale to be the same at all points and in all directions throughout the chart.

Straight Line

The rhumb line and the great circle are the two curves that a navigator might wish to have represented on a map as straight lines. The only projection that shows all rhumb lines as straight lines is the Mercator. The only projection that shows all great circles as straight lines is the gnomonic projection. However, this is not a conformal projection and cannot be used directly for obtaining direction or distance. No conformal chart represents all great circles as straight lines.

True Azimuth

It would be extremely desirable to have a projection that showed directions or azimuths as true throughout the chart. This would be particularly important to the navigator, who must determine from the chart the heading to be flown. There is no chart projection representing true great circle direction along a straight line from all points to all other points.

Coordinates Easy to Locate

The geographic latitudes and longitudes of places should be easily found or plotted on the map when the latitudes and longitudes are known.

Chart Projections

Chart projections may be classified in many ways. In this book, the various projections are divided into three classes according to the type of developable surface to which the projections are related. These classes are azimuthal, cylindrical, and conical.

Azimuthal Projections

An azimuthal, or zenithal projection, is one in which points on the earth are transferred directly to a plane tangent to the earth. According to the positioning of the plane and the point of projection, various geometric projections may be derived. If the origin of the projecting rays (point of projection) is the center of the sphere, a gnomonic projection results. If it is located on the surface of the earth opposite the point of the tangent plane, the projection is a stereographic, and if it is at infinity, an orthographic projection results. Figure 1-20 shows these various points of projection.

Figure 1-20. Azimuthal projections. [click image to enlarge]Gnomonic Projection

All gnomonic projections are direct perspective projections. Since the plane of every great circle cuts through the center of the sphere, the point of projection is in the plane of every great circle. This property then becomes the most important and useful characteristic of the gnomonic projection. Each and every great circle is represented by a straight line on the projection. A complete hemisphere cannot be projected onto this plane because points 90° from the center of the map project lines parallel to the plane of projection. Because the gnomonic is nonconformal, shapes or land masses are distorted, and measured angles are not true. At only one point, the center of the projection, are the azimuths of lines true. At this point, the projection is said to be azimuthal. Gnomonic projections are classified according to the point of tangency of the plane of projection. A gnomonic projection is polar gnomonic when the point of tangency is one of the poles, equatorial gnomonic when the point of tangency is at the equator and any selected meridian. [Figure 1-21]

Figure 1-21. Polar gnomonic and stereographic projections. [click image to enlarge]Stereographic Projection

The stereographic projection is a perspective conformal projection of the sphere. The term oblique stereographic is applied to any stereographic projection where the center of the projection is positioned at any point other than the geographic poles or the equator. If the center is coincident with one of the poles of the reference surface, the projection is called polar stereographic. The illustration in Figure 1-21 shows both gnomonic and stereographic projections. If the center lies on the equator, the primitive circle is a meridian, which gives the name meridian stereographic or equatorial stereographic.

Cylindrical Projections

The only cylindrical projection used for navigation is the Mercator, named after its originator, Gerhard Mercator (Kramer), who first devised this type of chart in the year 1569. The Mercator is the only projection ever constructed that is conformal and, at the same time, displays the rhumb line as a straight line. It is used for navigation, for nearly all atlases (a word coined by Mercator), and for many wall maps.

Imagine a cylinder tangent to the equator, with the source of projection at the center of the earth. It would appear much like the illustration in Figure 1-22, with the meridians being straight lines and the parallels being unequally spaced circles around the cylinder. It is obvious from Figure 1-22 that those parts of the terrestrial surface close to the poles could not be projected unless the cylinder was tremendously long, and the poles could not be projected at all.

Figure 1-22. Cylindrical projection.

On the earth, the parallels of latitude are perpendicular to the meridians, forming circles of progressively smaller diameters as the latitude increases. On the cylinder, the parallels of latitude are shown perpendicular to the projected meridians but, since the diameter of a cylinder is the same at any point along the longitudinal axis, the projected parallels are all the same length. If the cylinder is cut along a vertical line (a meridian) and spread flat, the meridians appear as equally spaced, vertical lines, and the parallels as horizontal lines, with distance between the horizontal lines increasing with distance away from the false (arbitrary) meridian.

The cylinder may be tangent at some great circle other than the equator, forming other types of cylindrical projections. If the cylinder is tangent at a meridian, it is a transverse cylindrical projection; if it is tangent at any point other than the equator or a meridian, it is called an oblique cylindrical projection. The patterns of latitude and longitude appear quite different on these projections because the line of tangency and the equator no longer coincide.

Charts and Projections (Part Two)

Mercator Projection

The Mercator projection is a conformal, nonperspective projection; it is constructed by means of a mathematical transformation and cannot be obtained directly by graphical means. The distinguishing feature of the Mercator projection among cylindrical projections is: At any latitude the ratio of expansion of both meridians and parallels is the same, thus, preserving the relationship existing on the earth. This expansion is equal to the secant of the latitude, with a small correction for the ellipticity of the earth. Since expansion is the same in all directions and since all directions and all angles are correctly represented, the projection is conformal.

Rhumb lines appear as straight lines and their directions can be measured directly on the chart. Distance can also be measured directly, but not by a single distance scale on the entire chart, unless the spread of latitude is small. Great circles appear as curved lines, concave to the equator or convex to the nearest pole. The shapes of small areas are very nearly correct, but are of increased size unless they are near the equator. [Figure 1-23] The Mercator projection has the following disadvantages:

1. Measuring large distances accurately is difficult.
2. Must apply conversion angle to great circle bearing before plotting.
3. Is useless above 80° N or below 80° S since the poles cannot be shown.

Figure 1-23. Mercator is conformal but not equal area.

The transverse or inverse Mercator is a conformal map designed for areas not covered by the equatorial Mercator.

With the transverse Mercator, the property of straight meridians and parallels is lost, and the rhumb line is no longer represented by a straight line. The parallels and meridians become complex curves and, with geographic reference, the transverse Mercator is difficult to use as a plotting chart. The transverse Mercator, though often considered analogous to a projection onto a cylinder, is in reality a nonperspective projection, constructed mathematically. This analogy, however, does permit the reader to visualize that the transverse Mercator shows scale correctly along the central meridian, which forms the great circle of tangency. [Figure 1-24] In effect, the cylinder has been turned 90° from its position for the ordinary Mercator, and a meridian, called the central meridian, becomes the tangential great circle. One series of NGA charts using this type of projection places the cylinder tangent to the 90° E–90° W longitude.

Figure 1-24. Transverse cylindrical projection—cylinder tangent at the poles. [click image to enlarge]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 constitutes the fictitious meridians, while a series of lines parallel to the plane of the tangent great circle forms the fictitious parallels.

On these projections, the fictitious graticule appears as the geographical one ordinarily appearing on the equatorial Mercator. That is, the fictitious meridians and parallels are straight lines perpendicular to each other. The actual meridians and parallels appear as curved lines, except the line of tangency. Geographical coordinates are usually expressed in terms of the conventional graticule. A straight line on the transverse Mercator projection makes the same angle with all fictitious meridians, but not with the terrestrial meridians. It is, therefore, a fictitious rhumb line.

The appearance of a transverse Mercator using the 90° E–90° W meridian as a reference or fictitious equator is shown in Figure 1-24. The dotted lines are the lines of the fictitious projection. The N–S meridian through the center is the fictitious equator, and all other original meridians are now curves concave on the N–S meridian with the original parallels now being curves concave to the nearer pole. To straighten the meridians, use the graph in Figure 1-25 to extract a correction factor that mathematically straightens the longitudes.

Figure 1-25. Transverse Mercator convergence graph. [click image to enlarge]Conic Projections

There are two classes of conic projections. The first is a simple conic projection constructed by placing the apex of the cone over some part of the earth (usually the pole) with the cone tangent to a parallel called the standard parallel and projecting the graticule of the reduced earth onto the cone. [Figure 1-26] The chart is obtained by cutting the cone along some meridian and unrolling it to form a flat surface. Notice, in Figure 1-27, the characteristic gap appears when the cone is unrolled. The second is a secant cone, cutting through the earth and actually contacting the surface at two standard parallels as shown in Figure 1-28.

Figure 1-26. Simple conic projection.Figure 1-27. Simple conic projection of northern hemisphere.Figure 1-28. Conic projection using secant cone.

Lambert Conformal (Secant Cone)

The Lambert conformal conic projection is of the conical type in which the meridians are straight lines that meet at a common point beyond the limits of the chart and parallels are concentric circles, the center of each being the point of intersection of the meridians. Meridians and parallels intersect at right angles. Angles formed by any two lines or curves on the earth’s surface are correctly represented. The projection may be developed by either the graphic or mathematical method. It employs a secant cone intersecting the spheroid at two parallels of latitude, called the standard parallels, of the area to be represented. The standard parallels are represented at exact scale. Between these parallels, the scale factor is less than unity and, beyond them, greater than unity. For equal distribution of scale error (within and beyond the standard parallels), the standard parallels are selected at one-sixth and five-sixths of the total length of the segment of the central meridian represented. The development of the Lambert conformal conic projection is shown by Figure 1-29.

Figure 1-29. Lambert conformal conic projection.

The chief use of the Lambert conformal conic projection is in mapping areas of small latitudinal width but great longitudinal extent. No projection can be both conformal and equal area but, by limiting latitudinal width, scale error is decreased to the extent the projection gives very nearly an equal area representation in addition to the inherent quality of conformality. This makes the projection very useful for aeronautical charts. Some of the advantages of the Lambert conformal conic projection are:

1. Conformality.
2. Great circles are approximated by straight lines (actually concave toward the midparallel).
3. For areas of small latitudinal width, scale is nearly constant. For example, the United States may be mapped with standard parallels at 33° N and 45° N with a scale error of only 2 percent for southern Florida. The maximum scale error between 30°30′ N and 47°30′ N is only one-half of 1 percent.
4. Positions are easily plotted and read in terms of latitude and longitude. Construction is relatively simple.
5. Its two standard parallels give it two lines of strength (lines along which elements are represented true to shape and scale).
6. Distance may be measured quite accurately. For example, the distance from Pittsburgh to Istanbul is 5,277 NM; distance as measured by the graphic scale on a Lambert projection (standard parallels 36° N and 54° N) without application of the scale factor is 5,258 NM; an error of less than 0.4 percent.

Some of the chief limitations of the Lambert Conformal conic projection are:

1. Rhumb lines are curved lines that cannot be plotted accurately.
2. Maximum scale increases as latitudinal width increases.
3. Parallels are curved lines (arcs of concentric circles).
4. Continuity of conformality ceases at the junction of two bands, even though each is conformal. If both have the same scale along their standard parallels, the common parallel (junction) has a different radius for each band and does not join perfectly.

Constant of the Cone

Most conic charts have the constant of the cone (convergence factor) computed and listed on the chart somewhere in the chart margin.

Convergence Angle (CA)

The convergence angle (CA) is the actual angle on a chart formed by the intersection of the Greenwich meridian and another meridian; the pole serves as the vertex of the angle. CAs, like longitudes, are measured east and west from the Greenwich meridian.

Convergence Factor (CF)

A chart’s convergence factor (CF) is a decimal number that expresses the ratio between meridional convergence as it actually exists on the earth and as it is portrayed on the chart. When the CA equals the number of the selected meridian, the chart CF is 1.0. When the CA is less than the number of the selected meridian, the chart CF is proportionately less than 1.0. The subpolar projection illustrated in Figure 1-30 portrays the standard parallels, 37° N and 65° N. It presents 360° of the earth’s surface on 282.726° of paper. Therefore, the chart has a CF of 0.78535 (282.726° divided by 360° equals 0.78535). Meridian 90° W forms a west CA of 71° with the Greenwich meridian.

Figure 1-30. A Lambert Conformal, convergence factor 0.78535.

Express as a formula:

CF × longitude = CA
0.78535 × 90° W = 71° west CA

Approximate a chart’s CF on subpolar charts by drawing a straight line covering 10 lines of longitude and measuring the true course at each end of the line, noting the difference between them, and dividing the difference by 10. NOTE: The quotient represents the chart’s CF.

Aeronautical Charts

An aeronautical chart is a pictorial representation of a portion of the earth’s surface upon which lines and symbols in a variety of colors represent features or details seen on the earth’s surface. In addition to ground image, many additional symbols and notes are added to indicate navigational aids (NAVAID) and data necessary for air navigation. Properly used, a chart is a vital adjunct to navigation; improperly used, it may become a hazard. Without it, modern navigation would never have reached its present state of development. Because of their great importance, the navigator must be thoroughly familiar with the wide variety of aeronautical charts and understand their many uses.

Lambert Conformal

Aeronautical charts are produced on many different types of projections. Since the demand for variety in charts is so great and the properties of the projections vary greatly, there is no one projection satisfying all navigation needs. The projection that most nearly answers all of the navigator’s problems is the Lambert conformal, and this projection is the one most widely used for aeronautical charts. An aeronautical chart of some projection and scale can be obtained for any portion of the earth.

Datums

Maps made by a given country traditionally use the datum created by that country. There may be as many as a thousand of these various datums in use throughout the world. Inherent problems result from over a hundred countries using widely different methods and standards to measure coordinate systems. When added to the effects of local variations in topography and the gravity field, systems are created that differ substantially from each other. These individualized datums are classified as local or regional.

The Department of Defense adopted a datum in 1987 called World Geodetic System 84 (WGS 84). This global datum is a system that models the entire planet, instead of one small piece. WGS 84 is used by NGA for production of almost all new maps and charts. The purpose of such a system is to minimize the confusion created by the proliferation of local datums. As long as all coordinates are stated in WGS 84, combat interoperability problems are minimized. In addition, WGS 84 positions may be computed from global positioning system (GPS) equipment to an extreme level of precision by NGA surveyors, well under half a meter anywhere in the world. Widespread use of WGS 84 virtually eliminates problems due to different datums.

It is important to realize that every coordinate is related to a specific datum. A latitude and longitude extracted from a WGS 84 chart is still a WGS 84 coordinate, and an MGRS point pulled from that same chart is also WGS 84. However, a ground survey of that same point could have established a local datum coordinate that is different from the map derived one by as much as a half mile. Always use the same datum throughout a mission, or serious positional errors are possible.

Scale

Obviously, charts are much smaller than the area they represent. The ratio between any given unit of length on a chart and the true distance it represents on the earth is the scale of the chart. The scale varies, and may vary greatly from one part of the chart to another. Charts are made to various scales for different purposes. If a chart is to show the whole world and yet not be too large, it must be drawn to small scale. If a chart is to show much detail, it must be drawn to a large scale; then it shows a smaller area than does a chart of the same size drawn to a small scale. Remember, large area, small scale; small area, large scale.

Aeronautical Chart

The scale of a chart may be given by a simple statement, such as 1 inch equals 10 miles. This means a distance of 10 miles on the earth’s surface is shown 1 inch long on the chart. On aeronautical charts, the scale is indicated in one of two ways: representative fraction or graphic scale.

Representative Fraction

The scale may be given as a representative fraction, such as 1:500,000 or 1/500,000. This means one of any unit on the chart represents 500,000 of the same unit on the earth. For example, 1 inch on the chart represents 500,000 inches on the earth. A representative fraction can be converted into a statement of miles to the inch. Thus, if the scale is 1:1,000,000, 1 inch on the chart stands for 1,000,000 inches or 1,000,000 divided by (6,076 × 12) equaling about 13.7 NM. Similarly, if the scale is 1:500,000, 1 inch on the chart represents about 6.86 NM. Thus, the larger the denominator of the representative fraction, the smaller the scale.

Graphic Scale

The graphic scale may be shown by a graduated line. It usually is found printed along the border of a chart. Take a measurement on the chart and compare it with the graphic scale of miles. The number of miles the measurement represents on the earth may be read directly from the graphic scale on the chart. The distance between parallels of latitude also provides a convenient scale for distance measurement. One degree of latitude always equals 60 NM and 1 minute of latitude always equals 1 NM.

Types of Charts

Aeronautical charts are differentiated on a functional basis by the type of information they contain. Navigation charts are grouped into three major types: general purpose, special purpose, and plotting. The name of the chart is a reasonable indication of its intended use. A Minimal Flight Planning Chart is primarily used in minimal flight planning techniques; a Jet Navigation Chart has properties making it adaptable to the speed, altitude, and instrumentation of jet aircraft. In addition to the specific type of information contained, charts vary according to the amount of information displayed. Charts designed to facilitate the planning of long distance flights carry less detail than those required for navigation en route. Local charts present great detail.

Standard Chart Symbols

Symbols are used for easy identification of information portrayed on aeronautical charts. While these symbols may vary slightly between various projections, the amount of variance is slight and, once the basic symbol is understood, variations of it are easy to identify. A chart legend is the key to explaining the meaning of the relief, culture, hydrography, vegetation, and aeronautical symbols. [Figure 1-31]

Figure 1-31. Sample chart legend. [click image to enlarge]

Relief (Hypsography)

Chart relief shows the physical features related to the differences in elevation of land surface. These include features, such as mountains, hills, plateaus, plains, depressions, etc. Standard symbols and shading techniques are used in relief portrayal on charts; these include contours, spot elevations and variations in tint, and shading to represent shadows.

Contour Lines

A contour line is a line connecting points of equal elevation. Figure 1-32 shows the relationship between contour lines and terrain. Notice on steep slopes the contours are close together and on gentle slopes they are farther apart. The interval of the contour lines usually depends upon the scale of the chart and the terrain depicted. In Figure 1-32, the contour interval is 1,000 feet. Depression contours are regular contour lines with spurs or ticks added on the down slope side.

Figure 1-32. Contour lines.

Spot Elevations

Spot elevations are the height of a particular point of terrain above an established datum, usually sea level.

Gradient Tints

The relief indicating contours is further emphasized on charts by a system of gradient tints. They are used to designate areas within certain elevation ranges by different color tints.

Shading

Perhaps the most obvious portrayal of relief is supplied by graduated shading applied to the southeastern side of elevated terrain and the northwestern side of depressions. This shading simulates the shadows cast by elevated features, lending a sharply defined, three-dimensional effect.

Cultural Features

All structural developments appearing on the terrain are known as cultural features. Three main factors govern the amount of detail given to cultural features: the scale of the chart, the use of the chart, and the geographical area covered. Populated places, roads, railroads, installations, dams, bridges, and mines are some of the many kinds of cultural features portrayed on aeronautical charts. The true representative size and shape of larger cities and towns are shown. Standardized coded symbols and type sizes are used to represent smaller population centers. Some symbols denoting cultural features are usually keyed in a chart legend. However, some charts use pictorial symbols which are self-explanatory.

Hydrography

In this category, aeronautical charts depict oceans, coast lines, lakes, rivers, streams, swamps, reefs, and numerous other hydrographic features. Open water may be portrayed by tinting or vignetting, or may be left blank.

Vegetation

Vegetation is not shown on most small scale charts. Forests and wooded areas in certain parts of the world are portrayed on some medium scale charts. On some large scale charts, park areas, orchards, hedgerows, and vineyards are shown. Portrayal may be by solid tint, vignette, or supplemented vignette.

Aeronautical Information

In the aeronautical category, coded chart symbols denote airfields, radio aids to navigation, commercial broadcasting stations, Air Defense Identification Zones (ADIZ), compulsory corridors, restricted airspace, warning notes, lines of magnetic variation, and special navigational grids. Some aeronautical information is subject to frequent change.

For economy of production, charts are retained in stock for various periods of time. To keep the charts current, only the stable kinds of information are printed on navigation charts.

NGA produces and distributes all aeronautical charts and Flight Information Publication (FLIP) documents. A summary of the typical charts is in Figure 1-33. Requisitions should indicate item identification and terminology for each item requested as listed in the catalog. List aeronautical charts by series in numerical or alphabetical sequence; list FLIP documents by type (en route, planning, terminal), title, and geographic area of coverage. Contact NGA or its squadrons and detachments for technical assistance in preparing statements of requirements. Addresses are listed in the NGA Catalog of Maps, Charts, and Related Products.

Figure 1-33. Summary of typical charts. [click image to enlarge]