The Geodetic Coordinate System

The geodetic terrestrial coordinates of latitude and longitude evolved in response to the requirements of navigation at sea, where identifiable landmarks may be absent for thousands of miles, and unobstructed visibility in good weather may permit identification of a landfall from a considerable distance. With this coordinate system, the earth has a North Pole and a South Pole that define its axis of rotation. This axis passes through Earth’s center. Any plane that passes through the center of the earth describes a circle on the surface called a great circle. The equator is the great circle described by the plane that passes perpendicular to the earth’s axis. The great circle of a plane that contains the earth’s axis is called a meridian. Meridians always run due north and south and converge at the poles. The Prime Meridian is the great circle that passes through Greenwich, England. Greenwich was assigned the Prime Meridian by treaty in 1884 in recognition of the work on astronomy and navigation performed at the Greenwich Royal Observatory.

The angular measurement or arc between the Prime Meridian and the local meridian passing through any other point on the planet’s surface is called the longitude (λ) of that point. Longitude is measured in degrees, minutes, and seconds of arc east or west of the Prime Meridian, from 0 degrees through 180 degrees. Longitude bears a special relationship to time. Within reasonable standards of accuracy, the earth rotates once about its axis every 24 hours. As such, Earth moves through 360 degrees of longitude in 24 hours, that is 15 degrees each hour and 1 degree every 4 minutes. It is this fact that establishes the conventions by which sundials work, clocks run, and time and distance are defined. It also forever links the modern practice of celestial position finding to the accurate keeping of time.

The angular measurement between the plane of the equator, as measured north or south from the center of the earth to a point on the surface, is the latitude (L) of that point (Figure 96-4). All points at the same latitude form what is called a parallel of latitude. Latitude is measured in degrees, minutes, and seconds of arc from 0 degrees through 90 degrees north or south. As such, the latitude of the equator is 0 degrees, whereas that of each pole is 90 degrees north or south. Every point on the surface of the earth is defined by a specific longitude and latitude.

FIGURE 96-4 Meridians of longitude (including the Prime Meridian) and parallels of latitude as measured north and south of the equator in degrees of arc from the center of the earth.

(With permission from the Department of the Air Force: Survival—training edition. Manual 64-3. Randolph Air Force Base, Tex, 1969, Air Training Command.)

A nautical mile (i.e., 1852 m, 6076 feet, 1.15 statute miles) is the distance on a great circle that covers an angle of 1 minute of arc as measured from the center of the earth. A degree of arc (60 minutes of arc) is thus 60 nautical miles, and 1 second of arc is equal to about 100 feet. It must be recognized that 1 minute of latitude will always equal 1 nautical mile, whereas 1 minute of longitude will only equal 1 nautical mile at the equator. At all points north or south of the equator, 1 minute of longitude will cover less than 1 nautical mile, as a result of the convergence of the meridians toward the poles. It should be obvious that, at either of Earth’s poles, one could walk through 360 degrees of longitude in only a few strides.

Latitude and longitude appear along the margins of topographic maps distributed by the United States Geological Survey (USGS) and by other national governmental organizations responsible for cartography. At each map corner, the latitude and longitude of the point defined by the intersection of the horizontal and vertical map margins is recorded in degrees, minutes, and seconds (Figure 96-5, online). On standard USGS 7.5- and 15-minute maps, latitude and longitude notations appear on the margins at intervals of 2.5 minutes of arc, and are marked with black tick marks on the inside edges of each margin.

FIGURE 96-5 Portion of a United States Geological Survey 1 : 24,000 map showing the blue Universal Transverse Mercator tick marks on the map margin that give values for false easting (716000 m E) and northing (4347000 m N). A 1 : 24000 Universal Transverse Mercator roamer scale is superimposed on the map. The points of intersection between the arms of the roamer scale and the map margin allow the grid reference for the point at the outside corner of the roamer scale to be read.

Although it is conceptually useful, the nautically based latitude and longitude system is less well suited to land navigation, where precision on the order of tens of meters is often required and visibility may be limited by terrain features and vegetation. In addition, calculation of a new position based on the direction and distance traveled from a known starting point requires intimidating mathematics in the geodetic system, and the interconversion of minutes or seconds of arc to meters or feet is cumbersome and confusing. For these reasons, the UTM grid or the Military Grid Reference System was adopted by the United States Defense Mapping Agency in 1947 to cope with the specific exigencies of maneuvering and delivering ordinance on land.

The Universal Transverse Mercator Coordinate System

The UTM and Military Grid Reference System grids are metric, make use of the transverse Mercator map projection in common with maps distributed by the USGS, and require no conversion between distances expressed as angles and linear measures of distance expressed in meters (m) or kilometers (km). UTM divides the earth’s surface from 80 degrees south latitude to 84 degrees north latitude into 60 south- to north-running zones arrayed around the surface of the planet like narrow slices of an orange. Each zone is 6 degrees wide in longitude. The zones are consecutively numbered from 1 through 60 beginning at an index line, the International Date Line, and progressing eastward. Each zone is subdivided from south to north in 8-degree increments of latitude (except the northernmost zone, which encompasses 12 degrees of latitude [i.e., 72 degrees north to 84 degrees north]). The south-to-north divisions of each zone are labeled consecutively and alphabetically from C through X, excluding the letters I and O to avoid confusion with the numbers 1 and 0 (Figure 96-6, online). In UTM, terrestrial coordinates are expressed in meters east of a false origin and north of a latitude index line. The false origin for any zone is an arbitrarily assigned south–north line 500,000 m (1,640,420 feet) to the west of the central meridian of the UTM zone of interest. Progress to the east of the false origin is termed false easting or simply easting. In the northern hemisphere, the latitude index is the equator. In the southern hemisphere, the latitude index is the southern limit of strip C (i.e., 80 degrees south latitude). Progress to the north of the latitude index is termed northing.^27,38,60

FIGURE 96-6 Map with the Universal Transverse Mercator grid overlaid on a portion of the Western Hemisphere. Zone 16 and row S are highlighted in light gray. The area of their intersection, designated as 16S, is highlighted in dark gray. The central meridian for this zone lies at 87 degrees west longitude. The uppermost right-hand corner of the map represents the area used in the examples involving Universal Transverse Mercator coordinates discussed in the text.

UTM coordinates are printed on all USGS maps produced during the past several decades. These appear as numbered blue tick marks occurring at 1-km intervals along the horizontal and vertical map margins. The numbers express UTM eastings and northings and thus increase from left to right and from bottom to top (i.e., to the right and up). By convention, the central meridian of each of the 60 UTM zones is assigned an easting value of 500000 m E (500,000 m east of the false origin of the zone). Easting values less than 500,000 thus lie west of the central meridian for the applicable UTM zone, and easting values of more than 500,000 lie east of the central meridian for the UTM zone in question. Slight overlap (i.e., 80 km) between adjacent zones prevents negative easting values from occurring. Similarly, easting values of more than 1,000,000 are never encountered; they would lie beyond the overlap into the next zone to the east. For the northern hemisphere, northing values are expressed as meters north of the equator, and range from zero to 10000000 m N (10,000,000 m north of the equator) (Figure 96-7). Negative values for northing are avoided for the southern hemisphere by labeling the equator as 10000000 m N and counting upward toward this number as one moves northward from the southern latitude index (i.e., 80 degrees south latitude).

FIGURE 96-7 Diagram of a representative Universal Transverse Mercator zone showing the false origin 500,000 m to the west of the central meridian of the zone. The zone extends from 80 degrees south latitude to 84 degrees north latitude and spans 6 degrees of longitude. Note that the equator forms the index line for reckoning northing for the northern hemisphere, whereas the southern limit of the zone forms the northing index for the southern hemisphere.

(Redrawn from Cole WP: Using the UTM grid system to record historic sites. http://www.cr.nps.gov/nr/publications/bulletins/nrb28/.)

On the horizontal margins of the map in the left upper and right lower corners, one of the last blue tick marks is labeled with a six-digit number in mixed large and small numerals (i.e., ⁷16⁰⁰⁰ m E in Figure 96-5, online). This refers to a line that is 716,000 m east of the false origin or 216,000 m east of the central meridian of the applicable UTM zone, because the false easting value is more than 500,000 (the central meridian in this example is in UTM Zone 16 at 87 degrees west longitude). Similarly, one of the blue tick marks at the right lower or left upper vertical margins of the map image is labeled with a multidigit number (i.e., ⁴³74⁰⁰⁰ m N for the left upper border), indicating a line 4,374,000 m north of the equator in UTM row S. Note that, within the six-digit false easting value and seven-digit northing value, the numerals in larger type represent thousands of meters or kilometers. UTM tick marks on a map margin between corners are labeled with three- or four-digit numbers. The last two digits, which are in large numerals, represent whole kilometers in relation to the UTM reference value given near the corner of the map. Thus, for practical purposes, when navigating within an area of several dozens to several hundreds of square kilometers, the UTM margin tick marks on any large-scale USGS map can be thought of as a simple kilometer scale. The long and intimidating numeric labels on the tick marks can be ignored (except to recognize that they indicate 1-km increments on the map margin).

Every point on the earth’s surface can be described by a unique false easting and northing value; this is described as a grid reference. Use of the UTM grid system for plotting position based on a map is actually much simpler than its conceptual framework would suggest. Position plotting is greatly assisted by using a specialized ruler called a roamer scale that is compatible with common USGS map scales (see Figure 96-5, online). Roamer scales are included on many baseplate compasses, can be easily made from a scrap of paper, or can be printed or purchased from Internet sources. The large graduations on a roamer scale generally denote 100-m increments, whereas the smaller divisions may represent a 10- or 20-m span. The steps for determining UTM coordinates for any point on a compatible map are:

When a degree of comfort with UTM coordinates is attained, navigation from point to point becomes much more intuitive than with latitude and longitude. Using the method just described, it is a simple matter to determine bearing and distance in meters between any two points on the map, to plot GPS waypoints on the map, or to identify a probable position based on dead reckoning from a known starting point. Note that it is standard for GPS receivers to be able to express the user’s position in any of several formats, including as UTM coordinates. A location near the author’s home has geodetic coordinates of 39 degrees and 15 minutes north latitude and 84 degrees and 30 minutes west longitude as determined by a commonly available inexpensive GPS receiver. With several simple key presses, the grid reference is expressed in UTM format as:

16S ⁰⁷16⁴⁶⁹

⁴³46⁶⁷⁷

This indicates that the location is in UTM Grid Zone 16S (Zone 16, Row S). The meridians bounding Zone 16 are 90 degrees west longitude on the west and 84 degrees west longitude on the east. Row S is bounded by 32 degrees north latitude to the south and 40 degrees north latitude to the north. The latitude and longitude boundaries of the identified zone and row include southwestern Ohio. The numbers specifying the unique location within the zone and row must be read, per UTM convention, to the right (easting) and then up (northing). The first seven-digit number indicates that the site of interest has a false easting value of ⁷16⁴⁶⁹ m E (i.e., 716,469 m east of the central meridian for the zone) or 469 m east of the 16-km tick mark on the horizontal margin of the relevant USGS map (see Figure 96-5, online). The second number indicates that the location has a northing value of ⁴³46⁶⁷⁷ m N (i.e., 4,346,677 m north of the equator) or 677 m north of the 46-km tick mark on the vertical map margin.

For navigation in the majority of wilderness activities, the area of interest fits within a single USGS 7.5-minute square, and accuracy to within 100 m is adequate. As such, the UTM coordinates used to describe a location can be abbreviated for simplicity, including only the whole kilometers (i.e., the larger two-digit numerals) and the small digit to their immediate right (representing hundreds of meters). Do not round the last digit upward. In the prior example, the location of interest would be described in abbreviated UTM notation as easting 16⁴, northing 46⁶ (i.e., about 400 m east of the 16 tick mark and about 600 m north of the 46 tick mark).⁸ Map usage involving the UTM coordinate system is greatly facilitated by drawing a 1-km by 1-km grid on the map using the UTM tick marks to define the whole-kilometer spacing of the grid lines.

In practice, GPS should be applied to a wilderness trek in the following manner. Before embarking on a trip, the user should choose a terrestrial coordinate system (i.e., UTM versus latitude and longitude) and then enter into the receiver the precise coordinates of various important landmarks on the intended route of travel. The coordinates of locations of interest can be obtained from a trail guide or from a topographic map. For reasons articulated earlier, UTM coordinates offer a substantive benefit for land navigation as compared with the geodetic coordinate system. The waypoints obtained in this manner are entered, labeled, and stored within the receiver’s memory. If a topographic map of the area of travel is available, a UTM grid should be drawn on the map using the method outlined previously. At the beginning of the trip, the location of the nearest town or source of assistance and the location of the trailhead where the trip is begun are entered as waypoints. The trip then progresses using the map, established trails, or the GPS receiver to follow the intended route. Tracks are recorded as the trip progresses. When pausing to camp, the position of the camp would be named and entered as yet another waypoint. At any time, the bearing and distance to any waypoint of interest are available to the user. If, in a spasm of self-reliance, the user decides to lay aside the GPS receiver and pursue traditional methods of navigation and he or she becomes lost, reactivation of the receiver will allow the direction and distance to safety to be immediately determined; the tracks to the last waypoint could be retraced, or the receiver could be used to guide the user by bearing and distance to the next waypoint on the route.

Highly capable GPS receivers, including WAAS-enabled receivers, are commonly available at prices of less than $100. They will fit into a shirt pocket, and have sufficient battery power for 10 to 30 hours of continuous usage. This is sufficient for weeks of navigation if power is used judiciously, and most models use commonly available AA or AAA batteries. Models that incorporate full-color onscreen topographic maps can be purchased for $200 to $500. Still, GPS suffers from important limitations. Dead batteries yield a useless receiver, so spare batteries should always be included when traveling. The receivers are relatively fragile, and many are not waterproof or even particularly water resistant. Obstruction of the sky by terrain features or heavy foliage may interfere with the reception of satellite signals, which may render the receiver unable to acquire a sufficient number of satellites to provide a fix. In an era of national security risk, selective availability could be reimplemented or WAAS could be restricted, with resultant degradation of the accuracy of recreational GPS. Still, GPS is unsurpassed with regard to ease of use, accuracy, and usefulness for wilderness navigation. When applied with common sense and a routine awareness of approximate location, even the simplest GPS receiver renders it virtually impossible to become lost and effectively eliminates many of the pathfinding challenges that are inherent to wilderness travel. However, reliance on GPS as the sole navigational resource for any wilderness expedition is a grave error. As with all high-technology methodology, GPS can be easily disabled. The more self-contained methods of navigation discussed in later sections of this chapter should be used whenever possible to maintain positional awareness and navigational skill in anticipation of the possibility that GPS may fail.

Magnetic Dip, Deviation, and Declination

The directional properties of the compass result from interactions between magnetized iron in the compass needle and magnetic lines of force generated by metals in the earth’s core. These lines of force have both a vertical and horizontal component. The vertical component is termed magnetic inclination or dip. Dip causes a compass needle to incline downward from horizontal, potentially to a degree that interferes with the ability of the needle or card to pivot freely. Dip is 90 degrees at the magnetic poles and 0 degrees at the magnetic equator. Most modern compasses are manufactured to compensate for the average dip that is likely to be encountered in the region of intended use. Others allow a small weight to be moved along the indicator needle to compensate for dip in any region of use.⁵⁵

The horizontal component of the magnetic lines of force causes the compass needle to point to the earth’s north magnetic pole. It is an unfortunate fact that the earth’s magnetic and geographic poles do not correspond in location. The earth’s magnetic lines of force are not straight lines; rather, they meander in an irregular fashion dictated by irregularities in the density of the core. The irregular directionality of the earth’s magnetic field is called magnetic declination. The compass needle is also influenced by local magnetic forces. These forces may result from natural sources such as ore deposits or from artificial sources such as ferromagnetic metals in vehicles, equipment, and clothing fasteners. Displacement of the compass needle resulting from local magnetic influences is termed deviation. As a result of magnetic declination and deviation, compasses point to geographic north only when used with care in selected locations. In general, compasses point northward but not exactly due north.

Direction in compass navigation is expressed in three ways: (1) true direction or direction measured in reference to the earth’s meridians and geographic poles; (2) magnetic direction or direction measured in reference to the earth’s magnetic poles; and (3) compass direction or direction measured by the magnetic compass. Magnetic direction varies from true direction by the sum of declination and deviation. Compass direction varies from magnetic direction by the quantity of deviation.^10,43 The definitions of magnetic and compass direction point out the necessity of minimizing preventable sources of compass deviation when taking bearings. For practical purposes, when preventable sources of deviation are minimized and the compass is used with caution, magnetic direction and compass direction can be considered to be equivalent.

Wandering lines of points with equal magnetic declination can be graphed on maps and charts; these are called isogonic lines. Lines representing points on the surface of the earth where the magnetic declination is zero, and where magnetic north and true north are aligned, are termed agonic lines. In the Americas, an agonic line follows a relatively straight and slanting course extending from the east coast of Victoria Island in north-central Canada through western Lake Superior, along the west coast of Florida, and traversing South America from the Gulf of Venezuela to the southeastern coast of Brazil. At locations east of the agonic line, the compass needle declines to the west (counterclockwise) of true north; at points west of the agonic line, the compass needle declines to the east (clockwise) of true north. By convention, magnetic declination is given a positive sign when east and a negative sign when west (Figure 96-8). Declination is quantified as the angle between true and magnetic north.

FIGURE 96-8 Schematic representation of North America showing declination at various locations as the difference between true north (i.e., “N” on the compass rim) and magnetic north (i.e., tip of the compass needle).

(With permission from Seidman D: The essential wilderness navigator, Camden, Me, 1995, Ragged Mountain Press.)

By way of example, in southwestern Ohio, the current magnetic declination is approximately negative 5 degrees or approximately 5 degrees west. This means that a compass needle actually points 5 degrees to the west of true north and that the true bearing given by the needle is 355 degrees when the needle points to 360 degrees on the compass rim. Any magnetic bearing taken with a compass will thus be 5 degrees greater than the true bearing. To correct from magnetic to true, 5 degrees must be subtracted from any indicated magnetic bearing.

The mnemonic “Declination east, compass bearing least; declination west, compass bearing greatest” may be helpful for converting magnetic direction to true direction when taking a bearing. In other words, to convert from magnetic to true while taking a bearing from the compass, add east declination to the compass bearing, or subtract west declination from the compass bearing. When taking a true bearing from a map and converting it to a compass bearing to follow in the environment, subtract east declination from the true bearing, or add west declination to the true bearing. Interconversion between magnetic and true bearings is an essential skill for compass navigation. Failure to recognize this relationship will result in significant errors when following a map route by compass, because directional references on the map are based on true direction. At a location where the magnetic declination is 10 degrees, travel over a straight course derived from a map and guided by a compass will result in a 0.18-mile error for each 1 mile traveled if declination is not considered.²⁶

Magnetic declination for any location can be determined by referencing the Isogonic Chart for Magnetic Declination, produced every 5 years by the USGS. In the United States, magnetic declination varies from 23 degrees East in Washington State to 22 degrees West in Maine (see Figure 96-8).¹² On standard USGS 7.5-minute and 15-minute squares, magnetic declination is indicated by a pointer next to the indicator for true north at the bottom of the map. If one does not have access to an isogonic chart, declination for any location in the northern hemisphere can be empirically determined with reasonable accuracy by comparing the magnetic bearing of north with the true bearing as indicated by the direction to the star Polaris. Polaris lies up to 45 minutes of arc (i.e., 0.75 degrees) away from true north at some times of day, but this offset is negligible for wilderness navigation situations. Declination at any location can also be determined by comparing the magnetic bearing of a prominent landmark with the true bearing between the observer’s known location and the location of the landmark as read from a map.⁷

Compass Types

The three compass types used in land navigation are the fixed-dial compass, magnetic card compass, and baseplate compass (Figure 96-9, online). The simplest compass is the fixed-dial, which uses a magnetized needle that is balanced on a pivot and enclosed in a case and that is graduated around its periphery into 360 degrees. The magnetic card compass uses a magnetized needle or wire fixed to a circular card that is graduated around its periphery from 0 degrees to 360 degrees. The housing of the compass is marked with a line called the lubber line that allows magnetic bearings to be determined when the line is pointed at an object of interest. The lensatic compass used by the military, which has a lens for magnification of the compass card and sights for alignment to distant objects, is a typical magnetic card compass. The most useful compass for land navigation is the baseplate compass,^26,35,46,57 which consists of a fixed-dial compass (or capsule) mounted to a baseplate in a manner that allows the capsule to rotate in relation to the baseplate. The baseplate is marked with a line used to indicate the direction of travel. This line functions in a manner identical to the lubber line of the magnetic card compass. The capsule of the compass has an orienting arrow inscribed on its lower surface that points to the graduation denoting north on the capsule rim. On different models, this graduation may be labeled “0°,” “360°,” or “N.” Rotation of the capsule such that the compass needle is superimposed on the orienting arrow and points to “N” on the capsule rim allows the user to easily read the magnetic bearing indicated by the direction-of-travel line. As long as the direction-of-travel line is followed and the needle remains superimposed on the orienting arrow, the user is assured of maintaining the desired magnetic bearing during travel.

FIGURE 96-9 The three basic compass types. From left to right: Fixed-dial compass, magnetic card compass, and baseplate compass. Note the deviation in indicated north resulting from local magnetic influences.

Many baseplate compasses allow the orienting arrow to be adjusted relative to the rim of the capsule to compensate for magnetic declination. When the orienting arrow of such a compass is adjusted to point to the bearing of magnetic north, the “N” graduation on the capsule rim will indicate true north when the compass needle aligns with the orienting arrow. All bearings as read on the capsule rim will now represent true—rather than magnetic—direction. Baseplate compasses have other features particularly suited for use with a map, including plotting scales, a straightedge, and often a protractor and magnifier.⁵⁷

Correction for declination when using a fixed-dial or magnetic card compass requires addition or subtraction of the declination, as appropriate, from the magnetic bearing indicated by the compass rim or lubber line.

Compass Use

A magnetic compass is used to establish cardinal directions, bearings for use in route finding, and back bearings for use in returning to a known starting location. The term back bearing refers to the reciprocal of the bearing followed on the outbound leg of a journey (i.e., outbound bearing minus 180 degrees) or the reciprocal of a measured bearing to a prominent terrain feature. Any route can be subdivided into legs that can be defined by magnetic bearing lines. Ideally each leg should pass between prominent and identifiable landmarks that will remain recognizable even in the dark or in poor weather. However, even when weather or lighting conditions prevent visual acquisition of the landmark from a distance, careful compass work should permit the user to reach an objective. Early during the course of travel over each leg, the observer should visually check the back bearing of the direction of travel to become familiar with the view of the starting point as it will appear on the return journey. If possible, the bearing and back bearing of each leg of a route, and the landmarks defining each leg, should be recorded on paper rather than trusted to memory.

Use of a compass in this manner permits the user to return easily to the desired direction of travel if an obstacle to the intended route is encountered. The course around the obstacle is recorded as a series of legs of known direction and estimated (by stride) length. When permitted by the terrain, right-angle detours are the simplest to follow. The user returns to the intended route by traveling the reciprocal of the course of the detour for the same distance as that required for bypass of the obstacle¹⁰ (Figure 96-10). Return to the intended course is greatly augmented by using natural ranges. A natural range is formed by two landmarks that lie along the same bearing line, with one end indicated by a landmark of intermediate distance from the viewer and one at a greater distance (e.g., a large tree or rock formation several kilometers from the viewer and the silhouette of a hill or mountain on the horizon). As the traveler deviates from the intended course, the near and far landmarks will fall out of line. When the traveler returns to the intended route, the objects forming the natural range will return to alignment.

FIGURE 96-10 Use of a compass to return to an intended route when faced with an obstacle. A course 90 degrees to the intended course is walked for a known number of steps, the obstacle is bypassed, and the original course is regained by walking the reciprocal course of the initial detour for the same distance.

(With permission from the Department of the Army: Map reading and land navigation. Field manual 21-26. Washington, DC, 1987, Headquarters, Department of the Army.)

Use of a compass with a map allows the user to orient the map to the environment and relate bearings taken from the map to bearings measured with the compass. Correction for declination is essential when the compass is used for this task if true bearings are to be used when plotting a route. However, there is no absolute need for the use of true bearings in navigation; it is important only that the map and compass agree. Agreement can be accomplished either by correcting the compass to the map or by correcting the map to the compass. If a baseplate compass with declination adjustment is used, it is relatively simple to correct the compass to the map and use true bearings for all subsequent travel. With all types of compasses, however, it is easiest to use magnetic bearings exclusively. If the declination is known or can be determined observationally, magnetic meridians can be drawn on the map to be used in place of the true meridians represented by the map margins (Figure 96-11, online). These magnetic meridians will form an angle with the true meridians equal to the declination angle. A map modified in this manner permits magnetic bearings (rather than true) to be taken from the map for use when following a course. The internal consistency of this method is always much less confusing than the method requiring conversion between true bearings and compass bearings. Because of the ease with which bearings may be taken from the map when it is marked with magnetic meridians, maps for use in navigational sports (e.g., orienteering) are prepared exclusively with magnetic meridians. Choice between the use of true versus magnetic bearings should be made in advance of travel to permit modification of the map. Plotting magnetic meridians on a map requires a pencil, straightedge, flat surface, and protractor; these items are unlikely to be available during a field emergency.^55,57

FIGURE 96-11 A United States Geological Survey 1 : 24,000 (7.5-minute) map modified with magnetic meridians (dark lines). The magnetic meridians reflect the 8 degrees west declination of the area represented on the map. The compass has been placed with its edge parallel to a magnetic meridian, and the compass capsule rotated such that the orienting arrow on the bottom of the capsule points to north on the map. The map and compass were then rotated in concert to align the compass needle and the orienting arrow. The map is now oriented to the terrain, and directions as indicated on the capsule rim represent magnetic bearings to objects in the environment.

To orient a map with a baseplate compass corrected for declination, the compass capsule is rotated such that “N” on the capsule rim is aligned with the direction-of-travel arrow. An edge of the baseplate parallel to the direction-of-travel arrow is then placed on one of the vertical borders of the map. The map, with the compass in place, is then rotated until the compass needle is superimposed on the orienting arrow on the base of the capsule. True north on the map is now aligned with true north on the planet.

To orient a map that has been modified with magnetic meridians using an uncompensated baseplate compass, the compass capsule is rotated until “N” on the capsule rim aligns with the direction-of-travel arrow. An edge of the compass parallel to the direction-of-travel arrow is placed on one of the magnetic meridians plotted on the map. The map, with the compass in place, is rotated until the compass needle is superimposed on the orienting arrow. True north on the map now corresponds with true north in the surrounding landscape.^26,46,55,57 If an uncompensated compass of another type is used, the north–south line of the compass face or lubber line is superimposed on a magnetic meridian, and the map and compass are rotated in concert until the indicator needle points to “N.”

To plot and follow a bearing using a baseplate compass and map, the map is held horizontally, and a straightedge of the baseplate parallel to the direction-of-travel arrow is placed on a line connecting the starting and ending points of the leg. The compass capsule is then rotated until the orienting arrow points to north as indicated on the map. The map and compass are held together and rotated until the compass needle is superimposed on the orienting arrow. The intersection of the direction-of-travel arrow and the capsule rim now indicates the bearing of the leg, and the direction-of-travel arrow points to the objective (Figure 96-12). To follow the bearing, the user walks in the direction indicated by the direction-of-travel arrow while keeping the compass needle and orienting arrow in alignment.

FIGURE 96-12 The steps for plotting and following a bearing using a map and compass. A, The current position (road junction at X ) and destination (watch tower at Y ) are identified. B, The compass is then placed on the map with an edge along the line connecting X and Y. C, The compass capsule is rotated so that the orienting arrow points north as indicated by the magnetic meridians drawn on the map. The compass is now oriented to the map. D, The compass and map are now held horizontally and rotated until the magnetic needle is superimposed on the orienting arrow. The map is now aligned to the environment, and the bearing to Y is indicated at the intersection of the compass capsule and the direction-of-travel arrow (240 degrees in this example). As long as the needle is kept superimposed on the orienting arrow, the direction-of-travel arrow will point toward the destination.

When a map is oriented to the environment, back bearings from landmarks that are visible both on the map and in the landscape can be used to obtain a positional fix by resection or triangulation.⁴⁶ Each back bearing from a landmark represents an LOP that can be plotted on the map. The point of crossing of two or more LOPs fixes the position of the observer (Figure 96-13). Alternatively, the intersection between the LOP represented by a bearing line and a shoreline, riverbank, road, firebreak, or ridgeline can be used to fix position on a map.

FIGURE 96-13 Establishing a magnetic fix by crossing the back bearings from two prominent landmarks. This process is known as resection.

Makeshift Compasses

A field-expedient compass can be fabricated with relative ease. Items containing iron, nickel, or cobalt are suitable for use as an indicator needle. Iron in the form of a steel needle, pin, wire, staple, or paper clip is most commonly available. Most of these items are magnetized as purchased. If not, they can be magnetized by stroking them on a magnet salvaged from an electric motor or radio speaker, on a magnetized screwdriver or similar item, or on a piece of silk. A dry cell also can be used to magnetize a needle by wrapping an insulated wire tightly around the needle and connecting the ends of the wire to the battery terminals for several minutes. There is a fire risk associated with shorting the battery terminals in this manner, and sparks and heat should be expected. Trial and error will often yield a suitable magnetizer. The indicator needle is floated in water by placing it on a wood chip, leaf, slip of paper, or small piece of cork or closed-cell foam. The container, which may be the cupped palm of the hand or a puddle, should be protected from the wind (Figure 96-14). A compass that has been so constructed will reliably indicate a magnetic north–south line. The absolute determination of direction may require external cues, such as the general direction of sunrise, sunset, or the position of the sun at midday.

FIGURE 96-14 A makeshift compass constructed from a plastic cup, straight pin, and foam packing peanut. Note the correspondence between north as indicated by the makeshift device and the commercial compass.

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