Document text
HEADQUARTERS
DEPARTMENT OF THE ARMY
FM 3-25.26 (FM 21-26)
MAP READING
AND
LAND NAVIGATION
DISTRIBUTION RESTRICTION: Approved for public release; distribution is unlimited.
FM 3-25.26 (FM 21-26)
FIELD MANUAL HEADQUARTERS
No. 3-25.26 DEPARTMENT OF THE ARMY
Washington, DC , 20 July 2001
MAP READING AND LAND NAVIGATION
CONTENTS
Page
PREFACE v
Part One
MAP READING
CHAPTER 1. TRAINING STRATEGY
1 - 1 . Building-Block Approach 1-1
1-2. Army wide Implementation 1-2
1- 3. Safety 1-2
CHAPTER 2. MAPS
2- 1. Definition 2-1
2-2. Purpose 2-1
2-3. Procurement 2-2
2-4. Security 2-3
2-5. Care 2-3
2-6. Categories 2-3
2-7. Military Map Substitutes 2-7
2- 8. Standards of Accuracy 2-8
CHAPTER 3. MARGINAL INFORMATION AND SYMBOLS
3 - 1 . Marginal Infonnation on a Military Map 3-1
3- 2. Additional Notes 3-5
3-3. Topographic Map Symbols 3-5
3-4. Military Symbols 3-6
3- 5. Colors Used on a Military Map 3-6
CHAPTER 4. GRIDS
4- 1. Reference System 4-1
4-2. Geographic Coordinates 4-1
4-3 . Military Grids 4-10
DISTRIBUTION RESTRICTION: Approved for public release; distribution is unlimited.
*This publication FM 3-25.26 supersedes FM 21-26, 7 May 1993.
FM 3-25.26
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4-4. United States Army Military Grid Reference System 4-12
4-5. Locate a Point Using Grid Coordinates 4-17
4-6. Locate a Point Using the US Army Military Grid
Reference System 4-21
4-7. Grid Reference Box 4-24
4-8. Other Grid Systems 4-25
4- 9. Protection of Map Coordinates and Locations 4-27
CHAPTER 5. SCALE AND DISTANCE
5- 1. Representative Fraction 5-1
5-2. Graphic (Bar) Scales 5-3
5 - 3 . Other Methods 5-11
CHAPTER 6. DIRECTION
6- 1 . Methods of Expressing Direction 6-1
6-2. Base Lines 6-1
6-3 . Azimuths 6-2
6-4. Grid Azimuths 6-4
6-5. Protractor 6-5
6-6. Declination Diagram 6-8
6-7. Intersection 6-14
6-8. Resection 6-16
6-9. Modified Resection 6-19
6- 10. Polar Coordinates 6-20
CHAPTER 7. OVERLAYS
7- 1. Purpose 7-1
7-2. Map Overlay 7-1
7- 3. Aerial Photograph Overlay 7-3
CHAPTER 8. AERIAL PHOTOGRAPHS
8- 1 . Comparison With Maps 8-1
8-2. Types 8-1
8-3. Types of Film 8-7
8-4. Numbering and Titling Information 8-7
8-5 . Scale Detennination 8-8
8-6. Indexing 8-10
8-7. Orienting of Photograph 8-13
8-8. Point Designation Grid 8-14
8-9. Identification of Photograph Features 8-17
8-10. Stereovision 8-18
FM 3-25.26 (FM 21-26)
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Part Two
LAND NAVIGATION
CHAPTER 9. NAVIGATION EQUIPMENT AND METHODS
9-1. Types of Compasses 9-1
9-2. Lensatic Compass 9-1
9-3 . Compass Handling 9-2
9-4. Using a Compass 9-3
9-5. Field-Expedient Methods 9-7
9- 6 . Global Positioning System 9-12
CHAPTER 10. ELEVATION AND RELIEF
10- 1. Definitions 10-1
10-2. Methods of Depicting Relief 10-1
10-3. Contour Intervals 10-2
10-4. Types of Slopes 10-5
10-5. Percentage of Slope 10-8
10-6. Terrain Features 10-11
10-7. Interpretation of Terrain Features 10-17
10- 8. Profiles 10-20
CHAPTER 11. TERRAIN ASSOCIATION
11- 1. Orienting the Map 11-1
11-2. Locations 11-6
11-3. T errain Association Usage 11-7
11-4. T actical Considerations 11-9
11-5. Movement and Route Selection 11-12
11-6. Navigation Methods 11-14
11- 7. Night Navigation 11-18
CHAPTER 12. MOUNTED LAND NAVIGATION
12- 1. Principles 12-1
12-2. Navigator's Duties 12-1
12-3. Movement 12-1
12-4. Terrain Association Navigation 12-3
12-5. Dead Reckoning Navigation 12-6
12-6. Stabilized Turret Alignment Navigation 12-7
12- 7. Combination Navigation 12-8
CHAPTER 13. NAVIGATION IN DIFFERENT TYPES OF TERRAIN
13- 1. Desert Terrain 13-1
13-2. Mountain T errain 13-4
13-3. Jungle Terrain 13-6
13-4. Arctic T errain 13-9
FM 3-25.26
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13- 5. Urban Areas 13-10
CHAPTER 14. UNIT SUSTAINMENT
14- 1. Set Up a Sustainment Program 14-1
14-2. Set Up a Train-the-Trainer Program 14-2
14-3. Set Up a Land Navigation Course 14-2
APPENDIX A. FIELD SKETCHING A- 1
APPENDIX B. MAP FOLDING TECHNIQUES B-l
APPENDIX C. UNITS OF MEASURE AND CONVERSION FACTORS C-l
APPENDIX D. JOINT OPERATIONS GRAPHICS D- 1
APPENDIX E. EXPORTABLE TRAINING MATERIAL E- 1
APPENDIX F . ORIENTEERIN G F-l
APPENDIX G. M2 COMPASS G-l
APPENDIX H. ADDITIONAL AIDS H- 1
APPENDIX I. FOREIGN MAPS I- 1
APPENDIX J. GLOBAL POSITIONING SYSTEM J- 1
APPENDIX K. PRECISION LIGHTWEIGHT GLOBAL POSITIONING
SYSTEM RECEIVER K-l
GLOS S ARY Glossary- 1
REFERENCES References- 1
INDEX Index- 1
FM 3-25.26
PREFACE
The purpose of this field manual is to provide a standardized source document for
Armywide reference on map reading and land navigation. This manual applies to every
soldier in the Anny regardless of service branch, MOS, or rank. This manual also contains
both doctrine and training guidance on these subjects. Part One addresses map reading and
Part Two, land navigation. The appendixes include a list of exportable training materials, a
matrix of land navigation tasks, an introduction to orienteering, and a discussion of several
devices that can assist the soldier in land navigation.
The proponent of this publication is the US Army Infantry School. Submit changes to
this publication on DA Form 2028 (Recommended Changes to Publications and Blank
Forms) directly to —
Commandant
US Anny Infantry School
ATTN: ATSH-IN-S3
Fort Benning, GA 31905-5596.
Lusanoh@benning . anny . mil
Unless this publication states otherwise, masculine nouns and pronouns do not refer
exclusively to men.
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FM 3-25.26
PART ONE
MAP READING
CHAPTER 1
TRAINING STRATEGY
This manual is in response to an Armywide need for a new map reading
and land navigation training strategy based on updated doctrine. This
chapter describes and illustrates this approach to teaching these skills.
1-1. BUILDING-BLOCK APPROACH
Institution courses are designed to prepare the soldier for a more advanced duty position in
his unit. The critical soldiering skills of move, shoot, and communicate must be trained,
practiced, and sustained at every level in the schools as well as in the unit. The map reading
and land navigation skills taught at each level are critical to the soldiering skills of the duty
position for which he is being school-trained. Therefore, they are also a prerequisite for a
critical skill at a more advanced level.
a. A soldier completing initial-entry training must be prepared to become a team
member. He must be proficient in the basic map reading and dead reckoning skills.
b. After completing the Primary Leadership Development Course (PLDC), a soldier
should be ready to be a team leader. This duty position requires expertise in the skills of map
reading, dead reckoning, and terrain association.
c. A soldier completing the Basic NCO Course (BNCOC) has been trained for the
squad leader position. Map reading and land navigation at skill level 3 requires development
of problem-solving skills; for example, route selection and squad tactical movement.
d. At skill level 4, the soldier completing the Advanced NCO Course (ANCOC) is
prepared to assume the duty position of platoon sergeant or operations NCO. Planning
tactical movements, developing unit sustainment, and making decisions are the important
land navigation skills at this level.
e. Officers follow similar progression. A new second lieutenant must have mastered
map reading and land navigation skills, and have an aptitude for dead reckoning and terrain
association.
(1) After completing the Officer Basic Course, the officer must be prepared to assume
the duties and responsibilities of a platoon leader. He is required to execute the orders and
operations of his commander. Map reading and land navigation at this level require
development of the problem-solving skills of route selection and tactical movement.
(2) After completing the Officer Advanced Course, the officer is prepared to assume the
duties and responsibilities of a company commander or primary staff officer. The
commander must plan and execute operations with full consideration to all aspects of
navigation. The staff officer must recommend battlefield placement of all administrative,
logistical, and personnel resources. These recommendations cannot be tactically sound
unless the estimate process includes a detailed analysis of the area of operations. This ability
requires expertise in all map reading and navigation skills to include the use of nonmilitary
maps, aerial photographs, and terrain analysis with respect to both friendly and enemy
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forces. The commander/staff officer must plan and execute a program to develop the unit's
train-the-trainer program for land navigation.
f. A program of demonstrated proficiency of all the preceding skill levels to the
specified conditions and standards is a prerequisite to the successful implementation of a
building-block training approach. This approach reflects duty position responsibilities in
map reading and land navigation. An understanding of the fundamental techniques of dead
reckoning or field-expedient methods is a basic survival skill that each soldier must develop
at the initial-entry level. This skill provides a support foundation for more interpretive
analysis at intennediate skill levels 2 and 3, with final progression to level 4. Mastery of all
map reading and land navigation tasks required in previous duty positions is essential for the
sequential development of increasingly difficult abilities. This building-block approach is
supported by scope statements. It is part of the training doctrine at each level in the
institutional training environment of each course.
g. Exportable training and instructor support/certification packages are being developed
based upon the updated map reading and land navigation field manual. Innovative training
devices and materials are being developed for use in the institution, ROTC regions, and the
field. (See Appendixes E and H.)
1-2. ARMYWIDE IMPLEMENTATION
A mandatory core of critical map reading and land navigation tasks and a list of electives
will be provided to each TRADOC service school and FORSCOM professional development
school. Standardization is achieved through the mandatory core. Exportable training material
is made available to support Armywide implementation.
1-3. SAFETY
Unit leaders plan to brief and enforce all safety regulations established by local range
control. They coordinate the mode of evacuation of casualties through the appropriate
channels. They review all installation safety regulations. Unit leaders must complete a
thorough terrain reconnaissance before using an area for land navigation training. They
should look for dangerous terrain, heavy trafficked roads, water obstacles, wildlife, and
training debris.
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CHAPTER 2
MAPS
Cartography is the art and science of expressing the known physical
features of the earth graphically by maps and charts. No one knows who
drew, molded, laced together, or scratched out in the dirt the first map. But
a study of history reveals that the most pressing demands for accuracy and
detail in mapping have come as the result of military needs. Today, the
complexities of tactical operations and deployment of troops are such that
it is essential for all soldiers to be able to read and interpret their maps in
order to move quickly and effectively on the battlefield. This chapter
includes the definition and purpose of a map and describes map security,
types, categories, and scales.
2-1. DEFINITION
A map is a graphic representation of a portion of the earth's surface drawn to scale, as seen
from above. It uses colors, symbols, and labels to represent features found on the ground.
The ideal representation would be realized if every feature of the area being mapped could
be shown in true shape. Obviously this is impossible, and an attempt to plot each feature true
to scale would result in a product impossible to read even with the aid of a magnifying glass.
a. Therefore, to be understandable, features must be represented by conventional signs
and symbols. To be legible, many of these must be exaggerated in size, often far beyond the
actual ground limits of the feature represented. On a 1:250,000 scale map, the prescribed
symbol for a building covers an area about 500 feet square on the ground; a road symbol is
equivalent to a road about 520 feet wide on the ground; the symbol for a single-track railroad
(the length of a cross-tie) is equivalent to a railroad cross-tie about 1 ,000 feet on the ground.
b. The portrayal of many features requires similar exaggeration. Therefore, the selection
of features to be shown, as well as their portrayal, is in accord with the guidance established
by the Defense Mapping Agency.
2-2. PURPOSE
A map provides infonnation on the existence, the location of, and the distance between
ground features, such as populated places and routes of travel and communication. It also
indicates variations in terrain, heights of natural features, and the extent of vegetation cover.
With our military forces dispersed throughout the world, it is necessary to rely on maps to
provide infonnation to our combat elements and to resolve logistical operations far from our
shores. Soldiers and materials must be transported, stored, and placed into operation at the
proper time and place. Much of this planning must be done by using maps. Therefore, any
operation requires a supply of maps; however, the finest maps available are worthless unless
the map user knows how to read them.
2-3. PROCUREMENT
Most military units are authorized a basic load of maps. Local command supplements to
AR 115-11 provide tables of initial allowances for maps. Map requisitions and distributions
are accomplished through the Defense Mapping Agency Hydrographic and Topographic
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Center's Office of Distribution and Services. In the division, however, maps are a
responsibility of the G2 section.
a. To order a map, refer to the DMA catalog located at your S2/G2 shop. Part 3 of this
catalog, Topographic Maps, has five volumes. Using the delineated map index, find the map
or maps you want based upon the location of the nearest city. With this information, order
maps using the following forms:
(1) Standard Form 344. It can be typed or handwritten; it is used for mailing or over-the-
counter service.
(2) Department of Defense Form 1348. Same as SF 344. You can order copies of only
one map sheet on each form.
(3) Department of Defense Form 1348M. This is a punch card form for AUDODIN
ordering.
(4) Department of Defense Form 173. This is a message form to be used for urgent
ordering.
With the exception of the message form (DD 173), the numbered sections of all forms are
the same. For example: In block 1, if you are in CONUS, enter “AOD,” if you are overseas,
enter “A04.” In block 2, use one of the following codes for your location.
LOCATION
CODE
Europe
CS7
Hawaii
HM9
Korea
WM4
Alaska
WC1
Panama
HMJ
CONUS
HM8
Your supply section will help you complete the rest of the fonn.
b. Stock numbers are also listed in map catalogs, which are available at division and
higher levels and occasionally in smaller units. A map catalog consists of small-scale maps
upon which the outlines of the individual map sheets of a series have been delineated.
Another document that is an aid to the map user is the gazetteer. A gazetteer lists all the
names appearing on a map series of a geographical area, a designation that identifies what
is located at that place name, a grid reference, a sheet number of the map upon which the
name appeared, and the latitude and longitude of the named features. Gazetteers are prepared
for maps of foreign areas only.
2-4. SECURITY
All maps should be considered as documents that require special handling. If a map falls into
unauthorized hands, it could easily endanger military operations by providing information
of friendly plans or areas of interest to the enemy. Even more important would be a map on
which the movements or positions of friendly soldiers were marked. It is possible, even
though the markings on a map have been erased, to determine some of the erased
information. Maps are documents that must not fall into unauthorized hands.
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a. If a map is no longer needed, it must be turned in to the proper authority. If a map is
in danger of being captured, it must be destroyed. The best method of destruction is by
burning it and scattering the ashes. If burning is not possible, the map can be torn into small
pieces and scattered over a wide area.
b. Maps of some areas of the world are subject to third party limitations. These are
agreements that pennit the United States to make and use maps of another country provided
these maps are not released to any third party without pennission of the country concerned.
Such maps require special handling.
c. Some maps may be classified and must be handled and cared for in accordance with
AR 380-5 and, if applicable, other local security directives.
2-5. CARE
Maps are documents printed on paper and require protection from water, mud, and tearing.
Whenever possible, a map should be carried in a waterproof case, in a pocket, or in some
other place where it is handy for use but still protected.
a. Care must also be taken when using a map since it may have to last a long time. If
it becomes necessary to mark a map, the use of a pencil is recommended. Use light lines so
they may be erased easily without smearing and smudging, or leaving marks that may cause
confusion later. If the map margins must be trimmed for any reason, it is essential to note
any marginal information that may be needed later, such as grid data and magnetic
declination.
b. Special care should be taken of a map that is being used in a tactical mission,
especially in small units; the mission may depend on that map. All members of such units
should be familiar with the map's location at all times.
c. Appendix B shows two ways of folding a map.
2-6. CATEGORIES
The DMA’s mission is to provide mapping, charting, and all geodesy support to the armed
forces and all other national security operations. DMA produces four categories of products
and services: hydrographic, topographic, aeronautical, and missile and targeting. Military
maps are categorized by scale and type.
a. Scale. Because a map is a graphic representation of a portion of the earth's surface
drawn to scale as seen from above, it is important to know what mathematical scale has been
used. You must know this to detennine ground distances between objects or locations on the
map, the size of the area covered, and how the scale may affect the amount of detail being
shown. The mathematical scale of a map is the ratio or fraction between the distance on a
map and the corresponding distance on the surface of the earth. Scale is reported as a
representative fraction with the map distance as the numerator and the ground distance as
the denominator.
map distance
Representative fraction (scale) =
ground distance
As the denominator of the representative fraction gets larger and the ratio gets smaller, the
scale of the map decreases. Defense Mapping Agency maps are classified by scale into three
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categories. They are small-, medium-, and large-scale maps (Figure 2-1). The terms "small
scale," "medium scale," and "large scale" may be confusing when read in conjunction
with the number. However, if the number is viewed as a fraction, it quickly becomes
apparent that 1:600,000 of something is smaller than 1:75,000 of the same thing. Therefore,
the larger the number after 1:, the smaller the scale of the map.
(1) Small. Those maps with scales of 1:1,000,000 and smaller are used for general
planning and for strategic studies (bottom map in Figure 2-1). The standard small-scale map
is 1 : 1,000,000. This map covers a very large land area at the expense of detail.
(2) Medium. Those maps with scales larger than 1:1,000,000 but smaller than 1:75,000
are used for operational planning (center map in Figure 2-1). They contain a moderate
amount of detail, but terrain analysis is best done with the large-scale maps described below.
The standard medium-scale map is 1:250,000. Medium scale maps of 1:100,000 are also
frequently encountered.
(3 ) Large. Those maps with scales of 1:75,000 and larger are used for tactical,
administrative, and logistical planning (top map in Figure 2-1). These are the maps that you
as a soldier or junior leader are most likely to encounter. The standard large-scale map is
1:50,000; however, many areas have been mapped at a scale of 1:25,000.
b. Types. The map of choice for land navigators is the 1:50, 000-scale military
topographic map. It is important, however, that you know how to use the many other
products available from the DMA as well. When operating in foreign places, you may
discover that DMA map products have not yet been produced to cover your particular area
of operations, or they may not be available to your unit when you require them. Therefore,
you must be prepared to use maps produced by foreign governments that may or may not
meet the standards for accuracy set by DMA. These maps often use symbols that resemble
those found on DMA maps but which have completely different meanings. There may be
other times when you must operate with the only map you can obtain. This might be a
commercially produced map run off on a copy machine at higher headquarters. In Grenada,
many of our troops used a British tourist map.
Figure 2-1. Scale classifications.
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(1) Planimetric Map. This is a map that presents only the horizontal positions for the
features represented. It is distinguished from a topographic map by the omission of relief,
normally represented by contour lines. Sometimes, it is called a line map.
(2) Topographic Map. This is a map that portrays terrain features in a measurable way
(usually through use of contour lines), as well as the horizontal positions of the features
represented. The vertical positions, or relief, are normally represented by contour lines on
military topographic maps. On maps showing relief, the elevations and contours are
measured from a specific vertical datum plane, usually mean sea level. Figure 3-1 shows a
typical topographic map.
(3) Photomap. This is a reproduction of an aerial photograph upon which grid lines,
marginal data, place names, route numbers, important elevations, boundaries, and
approximate scale and direction have been added. (See Chapter 8.)
(4) Joint Operations Graphics. These maps are based on the format of standard
1 :250,000 medium-scale military topographic maps, but they contain additional information
needed in joint air-ground operations (Figure 2-2). Along the north and east edges of the
graphic, detail is extended beyond the standard map sheet to provide overlap with adjacent
sheets. These maps are produced both in ground and air fonnats. Each version is identified
in the lower margin as either Joint Operations Graphic (Air) or Joint Operations Graphic
(Ground). The topographic information is identical on both, but the ground version shows
elevations and contour in meters and the air version shows them in feet. Layer (elevation)
tinting and relief shading are added as an aid to interpolating relief. Both versions emphasize
airlanding facilities (shown in purple), but the air version has additional symbols to identify
aids and obstructions to air navigation. (See Appendix D for additional infonnation.)
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Figure 2-2. Joint operations graphic (air).
(5) Photomosaic. This is an assembly of aerial photographs that is commonly called a
mosaic in topographic usage. Mosaics are useful when time does not pennit the compilation
of a more accurate map. The accuracy of a mosaic depends on the method employed in its
preparation and may vary from simply a good pictorial effect of the ground to that of a
planimetric map.
(6) Terrain Model. This is a scale model of the terrain showing features, and in large-
scale models showing industrial and cultural shapes. It provides a means for visualizing the
terrain for planning or indoctrination purposes and for briefing on assault landings.
(7) Military City Map. This is a topographic map (usually at 1 : 12,550 scale, sometimes
up to 1:5,000), showing the details of a city. It delineates streets and shows street names,
important buildings, and other elements of the urban landscape important to navigation and
military operations in urban terrain. The scale of a military city map depends on the
importance and size of the city, density of detail, and available intelligence information.
(8) Special Maps. These are maps for special purposes, such as trafficability,
communications, and assault maps. They are usually in the fonn of an overprint in the scales
smaller than 1 : 100,000 but larger than 1 : 1 ,000,000. A special purpose map is one that has
been designed or modified to give information not covered on a standard map. The wide
range of subjects that could be covered under the heading of special purpose maps prohibits,
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within the scope of this manual, more than a brief mention of a few important ones. Some
of the subjects covered are:
• Terrain features.
• Drainage characteristics.
• Vegetation.
• Climate.
• Coasts and landing beaches.
• Roads and bridges.
• Railroads.
• Airfields.
• Urban areas.
• Electric power.
• Fuels.
• Surface water resources.
• Ground water resources.
• Natural construction materials.
• Cross-country movements.
• Suitability for airfield construction.
• Airborne operations.
2-7. MILITARY MAP SUBSTITUTES
If military maps are not available, use substitute maps. The substitute maps can range from
foreign military or commercial maps to field sketches. The DMA can provide black and
white reproductions of many foreign maps and can produce its own maps based upon
intelligence.
a. Foreign Maps. These are maps that have been compiled by nations other than our
own. When these must be used, the marginal information and grids are changed to conform
to our standards if time pennits. The scales may differ from our maps, but they do express
the ratio of map distance to ground distance and can be used in the same way. The legend
must be used since the map symbols almost always differ from ours. Because the accuracy
of foreign maps varies considerably, they are usually evaluated in regard to established
accuracy standards before they are issued to our troops. (See Appendix I for additional
information.)
b. Atlases. These are collections of maps of regions, countries, continents, or the world.
Such maps are accurate only to a degree and can be used for general infonnation only.
c. Geographic Maps. These maps give an overall idea of the mapped area in relation
to climate, population, relief, vegetation, and hydrography. They also show general location
of major urban areas.
d. Tourist Road Maps. These are maps of a region in which the main means of
transportation and areas of interest are shown. Some of these maps show secondary networks
of roads, historic sites, museums, and beaches in detail. They may contain road and time
distance between points. Careful consideration should be exercised about the scale when
using these maps.
e. City/Utility Maps. These are maps of urban areas showing streets, water ducts,
electricity and telephone lines, and sewers.
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f. Field Sketches. These are preliminary drawings of an area or piece of terrain. (See
Appendix A.)
g. Aerial Photographs. These can be used as map supplements or substitutes to help
you analyze the terrain, plan your route, or guide your movement. (See Chapter 8 for
additional information).
2-8. STANDARDS OF ACCURACY
Accuracy is the degree of conformity with which horizontal positions and vertical values are
represented on a map in relation to an established standard. This standard is detennined by
the DMA based on user requirements. A map can be considered to meet accuracy
requirement standards unless otherwise specified in the marginal infonnation.
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CHAPTER 3
MARGINAL INFORMATION AND SYMBOLS
A map could be compared to any piece of equipment, in that before it is
placed into operation the user must read the instructions. It is important that
you, as a soldier, know how to read these instructions. The most logical
place to begin is the marginal information and symbols, where useful
information telling about the map is located and explained. All maps are not
the same, so it becomes necessary every time a different map is used to
examine the marginal information carefully.
3-1. MARGINAL INFORMATION ON A MILITARY MAP
Figure 3-1 (page 3-4) shows a reduced version of a large-scale topographic map. The circled
numbers indicate the items of marginal infonnation that the map user needs to know. These
circled numbers correspond to the following listed items.
a. Sheet Name (1). The sheet name is found in bold print at the center of the top and
in the lower left area of the map margin. A map is generally named for the settlement
contained within the area covered by the sheet, or for the largest natural feature located
within the area at the time the map was drawn.
b. Sheet Number (2). The sheet number is found in bold print in both the upper right
and lower left areas of the margin, and in the center box of the adjoining sheets diagram,
which is found in the lower right margin. It is used as a reference number to link specific
maps to overlays, operations orders, and plans. For maps at 1 : 100,000 scale and larger, sheet
numbers are based on an arbitrary system that makes possible the ready orientation of maps
at scales of 1:100,000, 1:50,000, and 1:25,000.
c. Series Name (3). The map series name is found in the same bold print as the sheet
number in the upper left corner of the margin. The name given to the series is generally that
of a major political subdivision, such as a state within the United States or a European
nation. A map series usually includes a group of similar maps at the same scale and on the
same sheet lines or format designed to cover a particular geographic area. It may also be a
group of maps that serve a common purpose, such as the military city maps.
d. Scale (4). The scale is found both in the upper left margin after the series name, and
in the center of the lower margin. The scale note is a representative fraction that gives the
ratio of a map distance to the corresponding distance on the earth's surface. For example,
the scale note 1 :50,000 indicates that one unit of measure on the map equals 50,000 units of
the same measure on the ground.
e. Series Number (5). The series number is found in both the upper right margin and
the lower left margin. It is a sequence reference expressed either as a four-digit numeral
(1125) or as a letter, followed by a three- or four-digit numeral (M661; T71 10).
f. Edition Number (6). The edition number is found in bold print in the upper right
area of the top margin and the lower left area of the bottom margin. Editions are numbered
consecutively; therefore, if you have more than one edition, the highest numbered sheet is
the most recent. Most military maps are now published by the DMA, but older editions of
maps may have been produced by the US Army Map Service. Still others may have been
drawn, at least in part, by the US Anny Corps of Engineers, the US Geological Survey, or
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FM 3-25.26
other agencies affiliated or not with the United States or allied governments. The credit line,
telling who produced the map, is just above the legend. The map information date is found
immediately below the word "LEGEND" in the lower left margin of the map. This date is
important when determining how accurately the map data might be expected to match what
you will encounter on the ground.
g. Index to Boundaries (7). The index to boundaries diagram appears in the lower or
right margin of all sheets. This diagram, which is a miniature of the map, shows the
boundaries that occur within the map area, such as county lines and state boundaries.
h. Adjoining Sheets Diagram (8). Maps at all standard scales contain a diagram that
illustrates the adjoining sheets. On maps at 1 : 100,000 and larger scales and at 1 : 1,000,000
scale, the diagram is called the index to adjoining sheets. It consists of as many rectangles
representing adjoining sheets as are necessary to surround the rectangle that represents the
sheet under consideration. The diagram usually contains nine rectangles, but the number
may vary depending on the locations of the adjoining sheets. All represented sheets are
identified by their sheet numbers. Sheets of an adjoining series, whether published or
planned, that are at the same scale are represented by dashed lines. The series number of the
adjoining series is indicated along the appropriate side of the division line between the
series.
i. Elevation Guide (9). This is normally found in the lower right margin. It is a
miniature characterization of the terrain shown. The terrain is represented by bands of
elevation, spot elevations, and major drainage features. The elevation guide provides the
map reader with a means of rapid recognition of major landforms.
j. Declination Diagram (10). This is located in the lower margin of large-scale maps
and indicates the angular relationships of true north, grid north, and magnetic north. On
maps at 1:250,000 scale, this information is expressed as a note in the lower margin. In
recent edition maps, there is a note indicating the conversion of azimuths from grid to
magnetic and from magnetic to grid next to the declination diagram.
k. Bar Scales (11). These are located in the center of the lower margin. They are rulers
used to convert map distance to ground distance. Maps have three or more bar scales, each
in a different unit of measure. Care should be exercised when using the scales, especially
in the selection of the unit of measure that is needed.
l. Contour Interval Note (12). This note is found in the center of the lower margin
normally below the bar scales. It states the vertical distance between adjacent contour lines
of the map. When supplementary contours are used, the interval is indicated. In recent
edition maps, the contour interval is given in meters instead of feet.
m. Spheroid Note (13). This note is located in the center of the lower margin.
Spheriods (ellipsoids) have specific parameters that define the X Y Z axis of the earth. The
spheriod is an integral part of the datum.
n. Grid Note (14). This note is located in the center of the lower margin. It gives
information pertaining to the grid system used and the interval between grid lines, and it
identifies the UTM grid zone number.
o. Projection Note (15). The projection system is the framework of the map. For
military maps, this framework is of the conformal type; that is, small areas of the surface of
the earth retain their true shapes on the projection; measured angles closely approximate true
values; and the scale factor is the same in all directions from a point. The projection note
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FM 3-25.26
is located in the center of the lower margin. Refer to DMA for the development
characteristics of the conformal-type projection systems.
(1) Between 80° south and 84° north, maps at scales larger than 1:500,000 are based on
the transverse Mercator projection. The note reads TRANSVERSE MERCATOR
PROJECTION.
(2) Between 80° south and 84° north, maps at 1:1,000,000 scale and smaller are based
on standard parallels of the lambert conformal conic projection. The note reads, for
example, LAMBERT CONFORMAL CONIC PROJECTIONS 36° 40’ N AND 39° 20’ N.
(3) Maps of the polar regions (south of 80° south and north of 84° north) at 1 : 1,000,000
and larger scales are based on the polar stereographic projection. The note reads POLAR
STEREOGRAPHIC PROJECTION.
p. Vertical Datum Note (16). This note is located in the center of the lower margin.
The vertical datum or vertical-control datum is defined as any level surface (for example,
mean sea level) taken as a surface of reference from which to determine elevations. In the
United States, Canada, and Europe, the vertical datum refers to the mean sea level surface.
However, in parts of Asia and Africa, the vertical-control datum may vary locally and is
based on an assumed elevation that has no connection to any sea level surface. Map readers
should habitually check the vertical datum note on maps, particularly if the map is used for
low-level aircraft navigation, naval gunfire support, or missile target acquisition.
q. Horizontal Datum Note (17). This note is located in the center of the lower margin.
The horizontal datum or horizontal-control datum is defined as a geodetic reference point
(of which five quantities are known: latitude, longitude, azimuth of a line from this point,
and two constants, which are the parameters of reference ellipsoid). These are the basis for
horizontal-control surveys. The horizontal-control datum may extend over a continent or
be limited to a small local area. Maps and charts produced by DMA are produced on 32
different horizontal-control data. Map readers should habitually check the horizontal datum
note on every map or chart, especially adjacent map sheets. This is to ensure the products
are based on the same horizontal datum. If products are based on different horizontal-control
data, coordinate transfonnations to a common datum must be perfonned. UTM coordinates
from the same point computed on different data may differ as much as 900 meters.
r. Control Note (18). This note is located in the center of the lower margin. It indicates
the special agencies involved in the control of the technical aspects of all the information
that is disseminated on the map.
s. Preparation Note (19). This note is located in the center of the lower margin. It
indicates the agency responsible for preparing the map.
t. Printing Note (20). This note is also located in the center of the lower margin. It
indicates the agency responsible for printing the map and the date the map was printed. The
printing data should not be used to determine when the map information was obtained.
u. Grid Reference Box (21). This box is normally located in the center of the lower
margin. It contains instructions for composing a grid reference.
v. Unit imprint and Symbol (22). The unit imprint and symbol is on the left side of
the lower margin. It identifies the agency that prepared and printed the map with its
respective symbol. This infonnation is important to the map user in evaluating the reliability
of the map.
w. Legend (23). The legend is located in the lower left margin. It illustrates and
identifies the topographic symbols used to depict some of the more prominent features on
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FM 3-25.26
the map. The symbols are not always the same on every map. Always refer to the legend
to avoid errors when reading a map.
Figure 3-1. Topographical map.
FM 3-25.26
3-2. ADDITIONAL NOTES
Not all maps contain the same items of marginal infonnation. Under certain conditions,
special notes and scales may be added to aid the map user. The following are examples:
a. Glossary. This is an explanation of technical tenns or a translation of tenns on maps
of foreign areas where the native language is other than English.
b. Classification. Certain maps require a note indicating the security classification.
This is shown in the upper and lower margins.
c. Protractor Scale. This scale may appear in the upper margin on some maps. It is
used to lay out the magnetic-grid declination for the map, which, in turn, is used to orient the
map sheet with the aid of the lensatic compass.
d. Coverage Diagram. On maps at scales of 1 : 100,000 and larger, a coverage diagram
may be used. It is normally in the lower or right margin and indicates the methods by which
the map was made, dates of photography, and reliability of the sources. On maps at
1:250,000 scale, the coverage diagram is replaced by a reliability diagram.
e. Special Notes (24). A special note is any statement of general information that
relates to the mapped area. It is normally found in the lower right margin. For example:
This map is red-light readable.
f. User's Note (25). This note is normally located in the lower right-hand margin. It
requests cooperation in correcting errors or omissions on the map. Errors should be marked
and the map forwarded to the agency identified in the note.
g. Stock Number Identification (26). All maps published by the DMA that are in the
Department of the Anny map supply system contain stock number identifications that are
used in requisitioning map supplies. The identification consists of the words "STOCK NO"
followed by a unique designation that is composed of the series number, the sheet number
of the individual map and, on recently printed sheets, the edition number. The designation
is limited to 15 units (letters and numbers). The first 5 units are allotted to the series
number; when the series number is less than 5 units, the letter "X" is substituted as the fifth
unit. The sheet number is the next component; however, Roman numerals, which are part
of the sheet number, are converted to Arabic numerals in the stock number. The last 2 units
are the edition number; the first digit of the edition number is a zero if the number is less
than 10. If the current edition number is unknown, the number 01 is used. The latest
available edition will be furnished. Asterisks are placed between the sheet number and the
edition number when necessary to ensure there are at least 1 1 units in the stock number.
h. Conversion Graph (27). Normally found in the right margin, this graph indicates
the conversion of different units of measure used on the map.
3-3. TOPOGRAPHIC MAP SYMBOLS
The purpose of a map is to permit one to visualize an area of the earth's surface with
pertinent features properly positioned. The map's legend contains the symbols most
commonly used in a particular series or on that specific topographic map sheet. Therefore,
the legend should be referred to each time a new map is used. Every effort is made to design
standard symbols that resemble the features they represent. If this is not possible, symbols
are selected that logically imply the features they portray. For example, an open-pit mining
operation is represented by a small black drawing of a crossed hammer and pickax.
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FM 3-25.26
a. Ideally, all the features within an area would appear on a map in their true proportion,
position, and shape. This, however, is not practical because many of the features would be
unimportant and others would be unrecognizable because of their reduction in size.
b. The mapmaker has been forced to use symbols to represent the natural and man-made
features of the earth’s surface. These symbols resemble, as closely as possible, the actual
features themselves as viewed from above. They are positioned in such a manner that the
center of the symbol remains in its true location. An exception to this would be the position
of a feature adjacent to a major road. If the width of the road has been exaggerated, then the
feature is moved from its true position to preserve its relation to the road. Field
Manual 21-31 gives a description of topographic features and abbreviations authorized for
use on our military maps.
3-4. MILITARY SYMBOLS
In addition to the topographic symbols used to represent the natural and man-made features
of the earth, military personnel require some method for showing identity, size, location, or
movement of soldiers; and military activities and installations. The symbols used to represent
these military features are known as military symbols. These symbols are not normally
printed on maps because the features and units that they represent are constantly moving or
changing; military security is also a consideration. They do appear in special maps and
overlays (Chapter 7). The map user draws them in, in accordance with proper security
precautions. Refer to FM 101-5-1 for complete information on military symbols.
3-5. COLORS USED ON A MILITARY MAP
By the fifteenth century, most European maps were carefully colored. Profile drawings of
mountains and hills were shown in brown, rivers and lakes in blue, vegetation in green, roads
in yellow, and special information in red. A look at the legend of a modern map confirms
that the use of colors has not changed much over the past several hundred years. To
facilitate the identification of features on a map, the topographical and cultural infonnation
is usually printed in different colors. These colors may vary from map to map. On a
standard large-scale topographic map, the colors used and the features each represent are:
a. Black. Indicates cultural (man-made) features such as buildings and roads, surveyed
spot elevations, and all labels.
b. Red-Brown. The colors red and brown are combined to identify cultural features,
all relief features, non-surveyed spot elevations, and elevation, such as contour lines on red-
light readable maps.
c. Blue. Identifies hydrography or water features such as lakes, swamps, rivers, and
drainage.
d. Green. Identifies vegetation with military significance, such as woods, orchards, and
vineyards.
e. Brown. Identifies all relief features and elevation, such as contours on older edition
maps, and cultivated land on red-light readable maps.
f. Red. Classifies cultural features, such as populated areas, main roads, and
boundaries, on older maps.
g. Other. Occasionally other colors may be used to show special infonnation. These
are indicated in the marginal information as a rule.
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FM 3-25.26
CHAPTER 4
GRIDS
This chapter covers how to determine and report positions on the ground
in terms of their locations on a map. Knowing where you are (position fixing j
and being able to communicate that knowledge is crucial to successful land
navigation as well as to the effective employment of direct and indirect fire,
tactical air support, and medical evacuation. It is essential for valid target
acquisition; accurate reporting of NBC contamination and various danger
areas; and obtaining emergency resupply. Few factors contribute as much
to the survivability of troops and equipment and to the successful
accomplishment of a mission as always knowing where you are. The chapter
includes explanations of geographical coordinates, Universal Transverse
Mercator grids, the military grid reference system, and the use of grid
coordinates.
4-1. REFERENCE SYSTEM
In a city, it is quite simple to find a location; the streets are named and the buildings have
numbers. The only thing needed is the address. However, finding locations in undeveloped
areas or in unfamiliar parts of the world can be a problem. To cope with this problem, a
uniform and precise system of referencing has been developed.
4-2. GEOGRAPHIC COORDINATES
One of the oldest systematic methods of location is based upon the geographic coordinate
system. By drawing a set of east-west rings around the globe (parallel to the equator), and
a set of north-south rings crossing the equator at right angles and converging at the poles,
a network of reference lines is formed from which any point on the earth's surface can be
located.
a. The distance of a point north or south of the equator is known as its latitude. The
rings around the earth parallel to the equator are called parallels of latitude or simply
parallels. Lines of latitude run east-west but north-south distances are measured between
them.
b. A second set of rings around the globe at right angles to lines of latitude and passing
through the poles is known as meridians of longitude or simply meridians. One meridian is
designated as the prime meridian. The prime meridian of the system we use runs through
Greenwich, England and is known as the Greenwich meridian. The distance east or west of
a prime meridian to a point is known as its longitude. Lines of longitude (meridians) run
north-south but east- west distances are measured between them (Figures 4-1 and 4-2, page
4-2).
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FM 3-25.26
Figure 4-1. Prime meridian and equator.
Figure 4-2. Reference lines.
c. Geographic coordinates are expressed in angular measurement. Each circle is divided
into 360 degrees, each degree into 60 minutes, and each minute into 60 seconds. The degree
is symbolized by °, the minute by ', and the second by Starting with 0° at the equator, the
parallels of latitude are numbered to 90° both north and south. The extremities are the north
pole at 90° north latitude and the south pole at 90° south latitude. Latitude can have the same
numerical value north or south of the equator, so the direction N or S must always be given.
Starting with 0°at the prime meridian, longitude is measured both east and west around the
world. Lines east of the prime meridian are numbered to 180° and identified as east
longitude; lines west of the prime meridian are numbered to 180° and identified as west
longitude. The direction E or W must always be given. The line directly opposite the prime
meridian, 180°, may be referred to as either east or west longitude. The values of geographic
coordinates, being in units of angular measure, will mean more if they are compared with
units of measure with which we are more familiar. At any point on the earth, the ground
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FM 3-25.26
distance covered by one degree of latitude is about 1 1 1 kilometers (69 miles); one second
is equal to about 30 meters (100 feet). The ground distance covered by one degree of
longitude at the equator is also about 111 kilometers, but decreases as one moves north or
south, until it becomes zero at the poles. For example, one second of longitude represents
about 30 meters (100 feet) at the equator; but at the latitude of Washington, DC, one second
of longitude is about 24 meters (78 feet). Latitude and longitude are illustrated in Figure 4-3.
d. Geographic coordinates appear on all standard military maps; on some they may be
the only method of locating and referencing a specific point. The four lines that enclose the
body of the map (neatlines) are latitude and longitude lines. Their values are given in degrees
and minutes at each of the four corners. On a portion of the Columbus map (Figure 4-4), the
figures 32° 15' and 84°45' appear at the lower right corner. The bottom line of this map is
latitude 32°15’00"N, and the line running up the right side is longitude 84°45’00"W. In
addition to the latitude and longitude given for the four corners, there are, at regularly spaced
intervals along the sides of the map, small tick marks extending into the body of the map.
Each of these tick marks is identified by its latitude or longitude value. Near the top of the
right side of the map is a tick mark and the number 20'. The full value for this tick marks is
32°20’00" of latitude. At one-third and two-thirds of the distance across the map from the
20' tick mark will be found a cross tick mark (grid squares 0379 and 9679) and at the far side
another 20’ tick mark. By connecting the tick marks and crosses with straight lines, a
32°20'00" line of latitude can be added to the map. This procedure is also used to locate the
32°25’00" line of latitude. For lines of longitude, the same procedure is followed using the
tick marks along the top and bottom edges of the map.
e. After the parallels and meridians have been drawn, the geographic interval (angular
distance between two adjacent lines) must be determined. Examination of the values given
at the tick marks gives the interval. For most maps of scale 1:25,000, the interval is 2'30".
For the Columbus map and most maps of scale 1:50,000, it is 5’00". The geographic
coordinates of a point are found by dividing the sides of the geographic square in which the
point is located into the required number of equal parts. If the geographic interval is 5’00"
and the location of a point is required to the nearest second, each side of the geographic
square must be divided into 300 equal parts (5’00" = 300"), each of which would have a
Approxi
location
COLUN
MAP
Figure 4-3. Latitude and longitude.
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FM 3-25.26
value of one second. Any scale or ruler that has 300 equal divisions and is as long as or
longer than the spacing between the lines may be used.
f. The following steps will detennine the geographic coordinates of Wilkinson
Cemetery (northwest of the town of Cusseta) on the Columbus map.
(1) Draw the parallels and meridians on the map that encloses the area around the
cemetery.
(2) Detennine the values of the parallels and meridians where the point falls.
Latitude 32°15’00" and 32°20’00".
Longitude 84°45'00" and 84°50’00".
(3) Detennine the geographic interval (5’00" = 300").
(4) Select a scale that has 300 small divisions or multiples thereof (300 divisions, one
second each; 150 divisions, two seconds each; 75 divisions, four seconds each, and so forth).
(5) To determine the latitude —
(a) Place the scale with the 0 of the scale on the latitude of the lowest number value
(32°15’00") and the 300 of the scale on the highest numbered line (32°20’00") (1,
Figure 4-4).
(b) While keeping the 0 and 300 on the two lines, slide the scale (2, Figure 4-4) along
the parallels until the Wilkinson Cemetery symbol is along the edge of the numbered scale.
(c) Read the number of seconds from the scale (3, Figure 4-4), about 246.
(d) Convert the number of seconds to minutes and seconds (246" = 4’06") and add to the
value of the lower numbered line (32°15’00" + 4’06" = 32°19’06") (4, Figure 4-4).
RESULTS:
• The latitude is 32° 19’06", but this is not enough.
• The latitude 32° 19’06" could be either north or south of the equator, so the letter N
or S must be added to the latitude. To determine whether it is N or S, look at the
latitude values at the edge of the map and find the direction in which they become
larger. If they are larger going north, use N; if they are larger going south, use S.
• The latitude for the cemetery is 32°19’06"N.
(6) Detennine the longitude, repeat the same steps but measure between lines of
longitude and use E and W. The geographic coordinates of Wilkinson Cemetery should be
about 32°19’06"N and 84°47’32"W (Figure 4-5, page 4-6).
g. To locate a point on the Columbus map (Figure 4-6, page 4-7) when knowing the
geographic coordinates, many of the same steps are followed. To locate 32°25’28"N and
84°50’56"W, first find the geographic lines within which the point falls: latitude 32°25’00"
and 32°30’0"; and longitude 84°50’00" and 84°55’00". Subtract the lower latitude/longitude
from the higher latitude/longitude.
(1) Place the 0 of the scale on the 32°25'00" line and the 300 on the 32°30’00". Make
a mark at the number 28 on the scale (the difference between the lower and higher latitude).
(2) Place the 0 of the scale on the 84°50'00" line and the 300 on the 84°50'55". Make a
mark at the number 56 on the scale (the difference between the lower and higher longitude.
(3) Draw a vertical line from the mark at 56 and a horizontal line from the mark at 28;
they intersect at 32 25’28”N and 84 50’56”W.
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FM 3-25.26
FM 3-25.26
Figure 4-5. Determining longitude.
6
FM 3-25.26
Figure 4-6. Determining geographic coordinates.
h. If you do not have a scale or ruler with 300 equal divisions or a map whose interval
is other than 5’00", use the proportional parts method. Following the steps determines the
geographic coordinates of horizontal control station 141.
(1) Locate horizontal control station 141 in grid square (GL0784) (Figure 4-7, page 4-9).
(2) Find a cross in grid square GL0388 and a tick mark in grid square GL1 188 with 25'.
(3) Find another cross in grid square GL0379 and a tick mark in grid square GL1 179
with 20'.
(4) Enclose the control station by connecting the crosses and tick marks. The control
station is between 20’ and 25' (Figure 4-7, page 4-9).
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FM 3-25.26
(5) With a boxwood scale, measure the distance from the bottom line to the top line that
encloses the area around the control station on the map (total distance) (Figure 4-7).
(6) Measure the partial distance from the bottom line to the center of the control station
(Figure 4-7). These straight-line distances are in direct proportion to the minutes and seconds
of latitude and are used to set up a ratio.
RESULTS:
• The total distance is 9,200 meters, and the partial distance is 5,125 meters
(Figure 4-7).
• With the two distances and the five-minute interval converted to seconds (300"),
detennine the minutes and seconds of latitude using the following formula:
■ 5,125 x300= 1,537,500
■ 1,537,500 -r 9,200 = 167
■ 167 -r 60 = 2’47"
■ Add 2’47" to 32°20’00" = 32°20’47"
(7) Follow the same procedures to determine minutes and seconds of longitude
(Figure 4-7).
RESULTS:
• The total distance is 7,830 meters, and the partial distance is 4,000 meters
(Figure 4-7).
■ 4,000x300= 1,200,000
- 1,200,000 -r 7,830 = 153
- 153 -r 60 = 2’33"
■ Add 2’33" to 84°45’ = 84°47’33"N
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FM 3-25.26
GL0388 H GRID SQUARE
CONTROL
STATION 141
GL1179
GL0379
GRID SQUARE
Figure 4-7. Using the proportional parts method.
(8) The geographic coordinates of horizontal control station 141 in grid square GL0784
are 32°22’47"N latitude and 84°47’33"W longitude.
NOTE: When computing formulas, round off totals to the nearest whole number in step 2.
In step 3, convert the fraction to seconds by multiplying the fraction by 60 and
rounding off if the total is not a whole number.
i. The maps made by some nations do not have their longitude values based on the
prime meridian that passes through Greenwich, England. Table 4-1, on page 4-10, shows the
prime meridians that may be used by other nations. When these maps are issued to our
soldiers, a note usually appears in the marginal information giving the difference between
our prime meridian and the one used on the map.
FM 3-25.26
Amsterdam, Netherlands
4°53’01”E
Athens, Greece
23°42’59”E
Batavia (Djakarta), Indonesia
106°48’28”E
Bern, Switzerland
7°26’22”E
Brussels, Belgium
4°22’06”E
Copenhagen, Denmark
12°34’40”E
Ferro (Hierro), Canary Islands
17°39’46”W
Helsinki, Finland
24°53’17”E
Istanbul, Turkey
28°58’50”E
Lisbon, Portugal
9°07’55”W
Madrid, Spain
3°4T15”W
Oslo, Norway
10°43’23”E
Paris, France
2°20’14”E
Pulkovo, Russia
30°19’39”E
Rome, Italy
12°27’08”E
Stockholm, Sweden
18°03’30”E
Tirane, Albania
19°46’45”E
Table 1. Table of prime meridians.
4-3. MILITARY GRIDS
An examination of the transverse Mercator projection, which is used for large-scale military
maps, shows that most lines of latitude and longitude are curved lines. The quadrangles
formed by the intersection of these curved parallels and meridians are of different sizes and
shapes, complicating the location of points and the measurement of directions. To aid these
essential operations, a rectangular grid is superimposed upon the projection. This grid (a
series of straight lines intersecting at right angles) furnishes the map reader with a system
of squares similar to the block system of most city streets. The dimensions and orientation
of different types of grids vary, but three properties are common to all military grid systems:
one, they are true rectangular grids; two, they are superimposed on the geographic
projection; and three, they permit linear and angular measurements.
a. Universal Transverse Mercator Grid. The UTM grid has been designed to cover
that part of the world between latitude 84°N and latitude 80°S, and, as its name implies, is
imposed on the transverse Mercator projection.
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FM 3-25.26
(1) Each of the 60 zones (6 degrees wide) into which the globe is divided for the grid has
its own origin at the intersection of its central meridian and the equator (Figure 4-8). The
grid is identical in all 60 zones. Base values (in meters) are assigned to the central meridian
and the equator, and the grid lines are drawn at regular intervals parallel to these two base
lines. With each grid line assigned a value denoting its distance from the origin, the problem
of locating any point becomes progressively easier. Normally, it would seem logical to
assign a value of zero to the two base lines and measure outward from them. This, however,
would require either that directions — -N, S, E, or W — be always given with distances, or that
all points south of the equator or west of the central meridian have negative values.
(2) This inconvenience is eliminated by assigning "false values" to the base lines,
resulting in positive values for all points within each zone. Distances are always measured
RIGHT and UP (east and north as the reader faces the map), and the assigned values are
called "false easting" and "false northing." (Figure 4-9, page 4-12). The false eating value
for each central meridian is 500,000 meters, and the false northing value for the equator is
0 meters when measuring in the northern hemisphere and 10,000,000 meters when
measuring in the southern hemisphere. The use of the UTM grid for point designation will
be discussed in detail in paragraph 4-4.
Figure 4-8. UTM grid zone location.
b. Universal Polar Stereographic Grid. The UPS grid is used to represent the polar
regions. (Figure 4-10, page 4-13)
(1) North Polar Area. The origin of the UPS grid applied to the north polar area is the
north pole. The "north-south" base line is the line formed by the 0-degree and 180-degree
meridians; the "east-west" base line is formed by the two 90-degree meridians.
(2) South Polar Area. The origin of the UPS grid in the south polar area is the south
pole. The base lines are similar to those of the north polar area.
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Figure 4-9. False eastings and northings for the UPS grid.
4-4. UNITED STATES ARMY MILITARY GRID REFERENCE SYSTEM
This grid reference system is designated for use with the UTM and UPS grids. The
coordinate value of points in these grids could contain as many as 15 digits if numerals alone
were used. The US military grid reference system reduces the length of written coordinates
by substituting single letters for several numbers. Using the UTM and the UPS grids, it is
possible for the location of a point (identified by numbers alone) to be in many different
places on the surface of the earth. With the use of the military grid reference system, there
is no possibility of this happening.
a. Grid Zone Designation. The world is divided into 60 grid zones, which are large,
regularly shaped geographic areas, each of which is given a unique identification called the
grid zone designation.
(1) UTM Grid. The first major breakdown is the division of each zone into areas 6° wide
by 8° high and 6° wide by 12° high. Remember, for the transverse Mercator projection, the
earth’s surface between 80°S and 84°N is divided into 60 N-S zones, each 6° wide. These
zones are numbered from west to east, 1 through 60, starting at the 180° meridian. This
surface is divided into 20 east-west rows in which 19 are 8° high and 1 row at the extreme
north is 12° high. These rows are then lettered, from south to north, C through X (I and O
were omitted). Any 6° by 8° zone or 6° by 12° zone is identified by giving the number and
letter of the grid zone and row in which it lies. These are read RIGHT and UP so the number
is always written before the letter. This combination of zone number and row letter
constitutes the grid zone designation. Columbus lies in zone 16 and row S, or in grid zone
designation 16S (Figure 4-8, page 4-1 1).
4-12
FM 3-25.26
(2) UPS Grid. The remaining letters of the alphabet, A, B, Y, and Z, are used for the
UPS grids. Each polar area is divided into two zones separated by the 0-180° meridian. In
the south polar area, the letter A is the grid zone designation for the area west of the 0-180°
meridian, and B for the area to the east. In the north polar area, Y is the grid zone
designation for the western area and Z for the eastern area (Figure 4-10).
Figure 4-10. Grid zone designation for UPS grid.
b. 100,000-Meter Square. Between 84°N and 80°S, each 6° by 8° or 6° by 12° zone
is covered by 100,000-meter squares that are identified by the combination of two
alphabetical letters. This identification is unique within the area covered by the grid zone
designation. The first letter is the column designation; the second letter is the row
designation (Figure 4-11, page 4-14). The north and south polar areas are also divided into
100,000-meter squares by columns and rows. A detailed discussion of the polar system can
be found in Technical Report 8358.1. The 100,000-meter square identification letters are
located in the grid reference box in the lower margin of the map.
4-13
FM 3-25.26
PLATE 12
96° 680.000m 9QO 500.000m 84°
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Figure 4-11. Grid zone designation and 100,000-meter
square identification.
c. Grid Coordinates. We have now divided the earth's surface into 6° by 8°
quadrangles, and covered these with 100,000-meter squares. The military grid reference of
a point consists of the numbers and letters indicating in which of these areas the point lies,
plus the coordinates locating the point to the desired position within the 100,000-meter
square. The next step is to tie in the coordinates of the point with the larger areas. To do this,
you must understand the following.
(1) Grid Lines. The regularly spaced lines that make the UTM and the UPS grid on any
large-scale maps are divisions of the 100,000-meter square; the lines are spaced at 10,000-
or 1,000-meter intervals (Figure 4-12). Each of these lines is labeled at both ends of the map
with its false easting or false northing value, showing its relation to the origin of the zone.
Two digits of the values are printed in large type, and these same two digits appear at
intervals along the grid lines on the face of the map. These are called the principal digits, and
represent the 10,000 and 1,000 digits of the grid value. They are of major importance to the
map reader because they are the numbers he will use most often for referencing points. The
smaller digits complete the UTM grid designation.
4-14
FM 3-25.26
96°oo‘ 3 29 3 30 3 31
28 000m g
Figure 4-12. Gridlines.
EXAMPLE: The first grid line north of the south-west corner of the Columbus map is
labeled 3570000m N. This means its false northing (distance north of the equator) is
3,570,000 meters. The principal digits, 70, identify the line for referencing points in the
northerly direction. The smaller digits, 35, are part of the false coordinates and are rarely
used. The last three digits, 000, of the value are omitted. Therefore, the first grid line east of
the south-west comer is labeled 689000m E. The principal digits, 89, identify the line for
referencing points in the easterly direction (Figure 4-13, page 4-16).
4-15
FM 3-25.26
*5*00’ 6g9000m.[
/91
*01* TIMtT t*
. r epared and published by th« Oafanta Mapping Agency
Topographic Canter, Washington, D. C.
LEGEND
HOAD DATA >973 — OTHER INFORMATION >973
Figure 4-13. Columbus map, southwest corner.
(2) Grid Squares. The north-south and east-west grid lines intersect at 90°, forming grid
squares. Normally, the size of one of these grid squares on large-scale maps is 1,000 meters
(1 kilometer).
(3) Grid Coordinate Scales. The primary tool for plotting grid coordinates is the grid
coordinate scale. The grid coordinate scale divides the grid square more accurately than can
be done by estimation, and the results are more consistent. When used correctly, it presents
less chance for making errors. GTA 5-2-12, 1981, contains four types of coordinate scales
(Figure 4-14).
4-16
FM 3-25.26
Figure 4-14. Coordinate scales.
(a) The 1:25,000/1:250,000 (lower right in figure) can be used in two different scale
maps, 1 :25,000 or 1 :250,000. The 1 :25,000 scale subdivides the 1 ,000-meter grid block into
10 major subdivisions, each equal to 100 meters. Each 100-meter block has five graduations,
each equal to 20 meters. Points falling between the two graduations can be read accurately
by the use of estimation. These values are the fourth and eighth digits of the coordinates.
Likewise, the 1:250,000 scale is subdivided in 10 major subdivisions, each equal to 1,000
meters. Each 1,000-meter block has five graduations, each equal to 200 meters. Points falling
between two graduations can be read approximately by the use of estimation.
(b) The 1:50,000 scale (upper left in Figure 4-14) subdivides the 1,000-meter block into
10 major subdivisions, each equal to 100 meters. Each 100-meter block is then divided in
half. Points falling between the graduations must be estimated to the nearest 10 meters for
the fourth and eighth digits of the coordinates.
(c) The 1 : 100,000 scale (lower left in Figure 4-14) subdivides the 1,000-meter grid block
into five major subdivisions of 200 meters each. Each 200-meter block is then divided in half
at 100-meter intervals.
4-5. LOCATE A POINT USING GRID COORDINATES
Based on the military principle for reading maps (RIGHT and UP), locations on the map can
be determined by grid coordinates. The number of digits represents the degree of precision
4-17
FM 3-25.26
to which a point has been located and measured on a map — the more digits the more precise
the measurement.
a. Without a Coordinate Scale. Determine grids without a coordinate scale by
referring to the north-south grid lines numbered at the bottom margin of any map. Then read
RIGHT to the north-south grid line that precedes the desired point (this first set of two digits
is the RIGHT reading). Then by referring to the east-west grid lines numbered at either side
of the map, move UP to the east-west grid line that precedes the desired point (these two
digits are the UP reading). Coordinate 1484 locate the 1,000-meter grid square in which
point X is located; the next square to the right would be 1584; the next square up would be
1485, and so forth (Figure 4-15). Locate the point to the nearest 100 meters using estimation.
Mentally divide the grid square in tenths, estimate the distance from the grid line to the point
in the same order (RIGHT and UP). Give complete coordinate RIGHT, then complete
coordinate UP. Point X is about two-tenths or 200 meters to the RIGHT into the grid square
and about seven- tenths or 700 meters UP.
RESULTS: The coordinates to the nearest 100 meters are 142847.
1385
1485
1585
X
1384
1484
1584
1383
1483
1583
14 15
Figure 4-15. Determining grids without coordinate point.
b. With a Coordinate Scale (1:25,000). In order to use the coordinate scale for
determining grid coordinates, ensure that the appropriate scale is being used on the
corresponding map, and that the scale is right side up. To ensure the scale is correctly
aligned, place it with the zero-zero point at the lower left comer of the grid square. Keeping
the horizontal line of the scale directly on top of the east-west grid line, slide it to the right
until the vertical line of the scale touches the point for which the coordinates are desired
(Figure 4-16). When reading coordinates, examine the two sides of the coordinate scale to
ensure that the horizontal line of the scale is aligned with the east-west grid line, and the
vertical line of the scale is parallel with the north-south grid line. Use the scale when
precision of more than 100 meters is required. To locate the point to the nearest 10 meters,
measure the hundredths of a grid square RIGHT and UP from the grid lines to the point.
Point X is about 17 hundredths or 170 meters RIGHT and 84 hundredths or 840 meters UP.
The coordinates to the nearest 10 meters are 14178484.
4-18
FM 3-25.26
Figure 4-16. Placing a coordinate scale on a grid.
NOTE: Care should be exercised by the map reader using the coordinate scale when the
desired point is located within the zero-zero point and the number 1 on the scale.
Always prefix a zero if the hundredths reading is less than 10. In Figure 4-17, the
desired point is reported as 14818407.
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4-19
FM 3-25.26
c. 1:50,000 Coordinating Scale. On the 1:50,000 coordinate scale, there are two sides:
vertical and horizontal. These sides are 1,000 meters in length. The point at which the sides
meet is the zero-zero point. Each side is divided into 10 equal 100-meter segments by a long
tick mark and number. Each 100-meter segment is subdivided into 50-meter segments by a
short tick mark (Figure 4-18). By using interpolation, mentally divide each 50-meter
segment into tenths. For example, a point that lies after a whole number but before a short
tick mark is identified as 10, 20, 30, or 40 meters and any point that lies after the short tick
mark but before the whole number is identified as 60, 70, 80, or 90 meters.
Figure 4-18. 1:50,000 coordinating scale.
d. Example of Obtaining an Eight-Digit Coordinate Using 1:50,000 Scale. To ensure
the scale is correctly aligned, place it with the zero-zero point at the lower left corner of the
grid square. Keeping the horizontal line of the scale directly on top of the east-west grid line,
slide the scale to the right until the vertical line of the scale touches the point for which the
coordinates are desired (Figure 4-19, page 4-21). Reading right, you can see that the point
lies 530 meters to the right into the grid square, which gives a right reading of 7853. Reading
up, you can see that the point lies 320 meters up into the grid square, giving an up reading
of 0032.
4-20
FM 3-25.26
EH78530032
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76 77 78 79
Figure 4-19. Example of obtaining an eight-digit coordinate
using 1:50,000 scale.
e. Recording and Reporting Grid Coordinates. Coordinates are written as one
continuous number without spaces, parentheses, dashes, or decimal points; they must always
contain an even number of digits. Therefore, whoever is to use the written coordinates must
know where to make the split between the RIGHT and UP readings. It is a military
requirement that the 100,000-meter square identification letters be included in any point
designation. Normally, grid coordinates are detennined to the nearest 100 meters (six digits)
for reporting locations. With practice, this can be done without using plotting scales. The
location of targets and other point locations for fire support are determined to the nearest
10 meters (eight digits).
NOTE: Special care should be exercised when recording and reporting coordinates.
Transposing numbers or making errors could be detrimental to military
operations.
4-6. LOCATE A POINT USING THE US ARMY MILITARY
GRID REFERENCE SYSTEM
There is only one rule to remember when reading or reporting grid coordinates — always read
to the RIGHT and then UP. The first half of the reported set of coordinate digits represents
the left-to-right (easting) grid label, and the second half represents the label as read from the
4-21
FM 3-25.26
bottom to top (northing). The grid coordinates may represent the location to the nearest 10-,
100-, or 1,000-meter increment.
a. Grid Zone. The number 16 locates a point within zone 16, which is an area 6° wide
and extends between 80°S latitude and 84°N latitude (Figure 4-8, page 4-11).
b. Grid Zone Designation. The number and letter combination, 16S, further locates
a point within the grid zone designation 16S, which is a quadrangle 6° wide by 8° high.
There are 19 of these quads in zone 16. Quad X, which is located between 72°N and 84°N
latitude, is 12° high (Figure 4-8, page 4-11).
c. 100,000-Meter Square Identification. The addition of two more letters locates a
point within the 100,000-meter grid square. Thus 16SGL (Figure 4-11, page 4-14) locates
the point within the 100,000-meter square GL in the grid zone designation 16S. For
information on the lettering system of 100,000-meter squares, see TM 5-241-1.
d. 10,000-Meter Square. The breakdown of the US Army military grid reference
system continues as each side of the 100,000-meter square is divided into 10 equal parts.
This division produces lines that are 10,000 meters apart. Thus the coordinates 16SGL08
would locate a point as shown in Figure 4-20. The 10,000-meter grid lines appear as index
(heavier) grid lines on maps at 1:100,000 and larger.
Figure 4-20. The 10,000-meter grid square.
4-22
FM 3-25.26
e. 1,000-Meter Square. To obtain 1,000-meter squares, each side of the 10,000-meter
square is divided into 10 equal parts. This division appears on large-scale maps as the actual
grid lines; they are 1,000 meters apart. On the Columbus map, using coordinates
16SGL0182, the easting 01 and the northing 82 gives the location of the southwest comer
of grid square 0182 or to the nearest 1,000 meters of a point on the map (Figure 4-21).
Figure 4-21. The 1,000-meter grid square.
f. 100-Meter Identification. To locate to the nearest 100 meters, the grid coordinate
scale can be used to divide the 1,000-meter grid squares into 10 equal parts (Figure 4-22,
page 4-24).
g. 10-Meter Identification. The grid coordinate scale has divisions every 50 meters
on the 1:50,000 scale and every 20 meters on the 1:25,000 scale. These can be used to
estimate to the nearest 10 meters and give the location of one point on the earth's surface to
the nearest 10 meters.
4-23
FM 3-25.26
EXAMPLE: 16SGL0 1948253 (gas tank) (Figure 4-22).
10 METERS
100 METERS
Figure 4-22. The 100-meter and 10-meter grid squares.
h. Precision. The precision of a point's location is shown by the number of digits in the
coordinates; the more digits, the more precise the location (Figure 4-22, insert).
4-7. GRID REFERENCE BOX
A grid reference box (Figure 4-23) appears in the marginal information of each map sheet.
It contains step-by-step instructions for using the grid and the US Army military grid
reference system. The grid reference box is divided into two parts.
a. The left portion identifies the grid zone designation and the 100,000-meter square.
If the sheet falls in more than one 100,000-meter square, the grid lines that separate the
squares are shown in the diagram and the letters identifying the 100,000-meter squares are
given.
EXAMPLE: On the Columbus map sheet, the vertical line labeled 00 is the grid line that
separates the two 100,000-meter squares, FL and GL. The left portion also shows a sample
for the 1 ,000-meter square with its respective labeled grid coordinate numbers and a sample
point within the 1,000-meter square.
b. The right portion of the grid reference box explains how to use the grid and is keyed
on the sample 1,000-meter square of the left side. The following is an example of the
military grid reference:
EXAMPLE: 16S locates the 6° by 8° area (grid zone designation).
4-24
FM 3-25.26
SAMPL
£ 1,000-METER GRID
SQUARE
100-METER REFERENCE
1 . Read large numbers labeling the VERTICAL grid
line left of point and estimate tenths (100-meters)
from grid line to point
2. Read large numbers labeling the HORIZONTAL
grid line below point and estimate (100-meters)
from grid line.
Example: 123456
x Sample
point
46
1
2 1
r 45
3
100,000-METER SQUARE IDENTIFICATION
FL | GL
7 00
WHEN REPORTING ACROSS A 100,000-METER
LINE, PREFIX THE 100,000-METER SQUARE
IDENTIFICATION, IN WHICH THE POINT UES.
Example: FL1 23456
GRID ZONE DESIGNATION
16S
WHEN REPORTING OUTSIDE THE GRID ZONE
DESIGNATION AREA, PREFIX THE GRID ZONE
DESIGNATION.
Example: 16SFL1 23456
Figure 4-23. Grid reference box.
4-8. OTHER GRID SYSTEMS
The military grid reference system is not universally used. Soldiers must be prepared to
interpret and use other grid systems, depending on the area of operations or the personnel
the soldiers are operating with.
a. British Grids. In a few areas of the world, British grids are still shown on military
maps. However, the British grid systems are being phased out. Eventually all military
mapping will be converted to the UTM grid.
b. World Geographic Reference System (GEOREF). This system is a worldwide
position reference system used primarily by the US Air Force. It may be used with any map
or chart that has latitude and longitude printed on it. Instructions for using GEOREF data
are printed in blue and are found in the margin of aeronautical charts (Figure 4-24,
page 4-26). This system is based upon a division of the earth's surface into quadrangles of
latitude and longitude having a systematic identification code. It is a method of expressing
latitude and longitude in a form suitable for rapid reporting and plotting. Figure 4-24
illustrates a sample grid reference box using GEOREF. The GEOREF system uses an
identification code that has three main divisions.
4-25
FM 3-25.26
Figure 4-24. Sample reference using GEOREF.
(1) First Division. There are 24 north-south (longitudinal) zones, each 15-degree wide.
These zones, starting at 180 degrees and progressing eastward, are lettered A through Z
(omitting I and O). The first letter of any GEOREF coordinate identifies the north-south zone
in which the point is located. There are 12 east-west (latitudinal) bands, each 15-degree
wide. These bands are lettered A through M (omitting I) northward from the south pole. The
second letter of any GEOREF coordinate identifies the east-west band in which the point is
located. The zones and bands divide the earth's surface into 288 quadrangles, each identified
by two letters.
(2) Second Division. Each 15-degree quadrangle is further divided into 225 quadrangles
of 1 degree each (15 degrees by 15 degrees). This division is effected by dividing a basic
15-degree quadrangle into 15 north-south zones and 15 east-west bands. The north-south
zones are lettered A through Q (omitting I and O) from west to east. The third letter of any
GEOREF coordinate identifies the 1 degree north-south zone within a 15-degree quadrangle.
The east-west bands are lettered A through Q (I and O omitted) from south to north. The
fourth letter of a GEOREF coordinate identifies the 1 degree east-west band within a
15-degree quadrangle. Four letters identify any 1 -degree quadrangle in the world.
4-26
FM 3-25.26
(3) Third Division. Each of the 1 -degree quadrangles is divided into 3,600 one -minute
quadrangles. These one-minute quadrangles are fonned by dividing the 1 -degree quadrangles
into 60 one-minute north-south zones numbered 0 through 59 from west to east, and 60
east- west bands numbered 0 to 59 from south to north. To designate any one of the 3,600
one -minute quadrangles requires four letters and four numbers. The rule READ RIGHT
AND UP is always followed. Numbers 1 through 9 are written as 01, 02, and so forth. Each
of the 1 -minute quadrangles may be further divided into 10 smaller divisions both north-
south and east-west, pennitting the identification of 0. 1 -minute quadrangles. The GEOREF
coordinate for any 0.1 -minute quadrangle consists of four letters and six numbers.
4-9. PROTECTION OF MAP COORDINATES AND LOCATIONS
A disadvantage of any standard system of location is that the enemy, if he intercepts one of
our messages using the system, can interpret the message and find our location. It is possible
and can be eliminated by using an authorized low-level numerical code to express locations.
Army Regulation 380-40 outlines the procedures for obtaining authorized codes.
a. The authorized numerical code provides a capability for encrypting map references
and other numerical information that requires short-tenn security protection when, for
operational reasons, the remainder of the message is transmitted in plain language. The
system is published in easy-to-use booklets with sufficient material in each for one month's
operation. Sample training editions of this type of system are available through the unit's
communications and electronics officer.
b. The use of any encryption methods other than authorized codes is, by regulation,
unauthorized and shall not be used.
4-27
FM 3-25.26
CHAPTER 5
SCALE AND DISTANCE
A map is a scaled graphic representation of a portion of the earth's
surface. The scale of the map permits the user to convert distance on the map
to distance on the ground or vice versa. The ability to determine distance on
a map, as well as on the earth's surface, is an important factor in planning
and executing military missions.
5-1. REPRESENTATIVE FRACTION
The numerical scale of a map indicates the relationship of distance measured on a map and
the corresponding distance on the ground. This scale is usually written as a fraction and is
called the representative fraction. The RF is always written with the map distance as 1 and
is independent of any unit of measure. (It could be yards, meters, inches, and so forth.) An
RF of 1/50,000 or 1:50,000 means that one unit of measure on the map is equal to 50,000
units of the same measure on the ground.
a. The ground distance between two points is determined by measuring between the
same two points on the map and then multiplying the map measurement by the denominator
of the RF or scale (Figure 5-1, page 5-2).
EXAMPLE:
The map scale is 1:50,000
RF = 1/50,000
The map distance from point A to point B is 5 units
5 x 50,000 = 250,000 units of ground distance
b. Since the distance on most maps is marked in meters and the RF is expressed in this
unit of measurement in most cases, a brief description of the metric system is needed. In the
metric system, the standard unit of measurement is the meter.
1 meter contains 100 centimeters (cm).
100 meters is a regular football field plus 10 meters.
1,000 meters is 1 kilometer (km).
10 kilometers is 10,000 meters.
Appendix C contains the conversion tables.
c. The situation may arise when a map or sketch has no RF or scale. To be able to
determine ground distance on such a map, the RF must be detennined. There are two ways
to do this:
(1) Comparison with Ground Distance.
(a) Measure the distance between two points on the map — map distance (MD).
(b) Detennine the horizontal distance between these same two points on the ground —
ground distance (GD).
(c) Use the RF formula and remember that RF must be in the general fonn:
RF = _J_ = MD
X GD
5-1
FM 3-25.26
Figure 5-1. Converting map distance to ground distance.
(d) Both the MD and the GD must be in the same unit of measure and the MD must be
reduced to 1.
EXAMPLE:
MD = 4.32 centimeters
GD = 2.16 kilometers
(216,000 centimeters)
RF = J_ = 4.32
X 216,000
or
216,000 = 50,000
4.32
therefore
RF = 1 or 1:50,000
50,000
( 2 ) Comparison With Another Map of the Same Area that Has an RF.
(a) Select two points on the map with the u nkn own RF. Measure the distance (MD)
between them.
(b) Locate those same two points on the map that have the known RF. Measure the
distance (MD) between them. Using the RF for this map, determine GD, which is the same
for both maps.
(c) Using the GD and the MD from the first map, detennine the RF using the formula:
RF= 1 = MD
X GD
5-2
FM 3-25.26
d. Occasionally it may be necessary to detennine map distance from a known ground
distance and the RF:
MD = GD
Denominator or RF
Ground Distance = 2,200 meters
RF = 1:50,000
MD = 2,200 meters
50,000
MD = 0.044 meters x 100 (centimeters per meter)
MD = 4.4 centimeters
e. When detennining ground distance from a map, the scale of the map affects the
accuracy. As the scale becomes smaller, the accuracy of measurement decreases because
some of the features on the map must be exaggerated so that they may be readily identified.
5-2. GRAPHIC (BAR) SCALES
A graphic scale is a ruler printed on the map and is used to convert distances on the map to
actual ground distances. The graphic scale is divided into two parts. To the right of the zero,
the scale is marked in full units of measure and is called the primary scale. To the left of the
zero, the scale is divided into tenths and is called the extension scale. Most maps have three
or more graphic scales, each using a different unit of measure (Figure 5-2). When using the
graphic scale, be sure to use the correct scale for the unit of measure desired.
EXTENSK
)N SCALE
PRIMAm
f SCALE
1 I
1000 500 0
Scale 1:50,000
1 2
3
4
1
5 Kilometers
1 i *
0
l
3
SUtwl* Miles
> *
0
1
7
3 Neutkel Miles
Figure 5-2. Using a graphic (bar) scale.
5-3
FM 3-25.26
a. To determine straight-line distance between two points on a map, lay a straight-edged
piece of paper on the map so that the edge of the paper touches both points and extends past
them. Make a tick mark on the edge of the paper at each point (Figure 5-3).
Figure 5-3. Transferring map distance to paper strip.
b. To convert the map distance to ground distance, move the paper down to the graphic
bar scale, and align the right tick mark (b) with a printed number in the primary scale so that
the left tick mark (a) is in the extension scale (Figure 5-4).
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FM 3-25.26
Figure 5-4. Measuring straight-line map distance.
c. The right tick mark (b) is aligned with the 3,000-meter mark in the primary scale,
thus the distance is at least 3,000 meters. To detennine the distance between the two points
to the nearest 10 meters, look at the extension scale. The extension scale is numbered with
zero at the right and increases to the left. When using the extension scale, always read right
to left (Figure 5-4). From the zero left to the beginning of the first shaded area is 100 meters.
From the beginning of the shaded square to the end of the shaded square is 100 to 200
meters. From the end of the first shaded square to the beginning of the second shaded square
is 200 to 300 meters. Remember, the distance in the extension scale increases from right to
left.
d. To determine the distance from the zero to tick mark (a), divide the distance inside
the squares into tenths (Figure 5-4). As you break down the distance between the squares in
the extension scale into tenths, you will see that tick mark (a) is aligned with the 950-meter
mark. Adding the distance of 3,000 meters determined in the primary scale to the 950 meters
you determined by using the extension scale, we find that the total distance between points
(a) and (b) is 3,950 meters.
e. To measure distance along a road, stream, or other curved line, the straight edge of
a piece of paper is used. In order to avoid confusion concerning the point to begin measuring
from and the ending point, an eight-digit coordinate should be given for both the starting and
ending points. Place a tick mark on the paper and map at the beginning point from which the
curved line is to be measured. Align the edge of the paper along a straight portion and make
a tick mark on both map and paper when the edge of the paper leaves the straight portion of
the line being measured (Figure 5-5A, page 5-7).
f. Keeping both tick marks together (on paper and map), place the point of the pencil
close to the edge of the paper on the tick mark to hold it in place and pivot the paper until
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FM 3-25.26
another straight portion of the curved line is aligned with the edge of the paper. Continue in
this manner until the measurement is completed (Figure 5-5B, page 5-7).
g. When you have completed measuring the distance, move the paper to the graphic
scale to determine the ground distance. The only tick marks you will be measuring the
distance between are tick marks (a) and (b). The tick marks in between are not used
(Figure 5-5C, page 5-7).
h. There may be times when the distance you measure on the edge of the paper exceeds
the graphic scale. In this case, there are different techniques you can use to determine the
distance.
(1) One technique is to align the right tick mark (b) with a printed number in the primary
scale, in this case the 5. You can see that from point (a) to point (b) is more than
6,000 meters when you add the 1,000 meters in the extension scale. To detennine the exact
distance to the nearest 10 meters, place a tick mark (c) on the edge of the paper at the end
of the extension scale (Figure 5-6A, page 5-8). You know that from point (b) to point (c) is
6,000 meters. With the tick mark (c) placed on the edge of the paper at the end of the
extension scale, slide the paper to the right. Remember the distance in the extension is
always read from right to left. Align tick mark (c) with zero and then measure the distance
between tick marks (a) and (c). The distance between tick marks (a) and (c) is 420 meters.
The total ground distance between start and finish points is 6,420 meters (Figure 5-6B,
page 5-8).
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FM 3-25.26
|l | II ^ \
\
(b)
-Distance from (a) to (b) is 4,250 meters
Figure 5-5. Measuring a curved line.
5-7
FM 3-25.26
Figure 5-6. Determining the exact distance.
(2) Another technique that may be used to determine exact distance between two points
when the edge of the paper exceeds the bar scale is to slide the edge of the paper to the right
until tick mark (a) is aligned with the edge of the extension scale. Make a tick mark on the
paper, in line with the 2,000-meter mark (c) (Figure 5-7 A). Then slide the edge of the paper
to the left until tick mark (b) is aligned with the zero. Estimate the 100-meter increments into
10-meter increments to determine how many meters tick mark (c) is from the zero line
(Figure 5-7B). The total distance would be 3,030 meters.
(3) At times you may want to know the distance from a point on the map to a point off
the map. In order to do this, measure the distance from the start point to the edge of the map.
The marginal notes give the road distance from the edge of the map to some towns,
highways, or junctions off the map. To detennine the total distance, add the distance
measured on the map to the distance given in the marginal notes. Be sure the unit of measure
is the same.
(4) When measuring distance in statute or nautical miles, round it off to the nearest one-
tenth of a mile and make sure the appropriate bar scale is used.
(5) Distance measured on a map does not take into consideration the rise and fall of the
land. All distances measured by using the map and graphic scales are flat distances.
Therefore, the distance measured on a map will increase when actually measured on the
ground. This must be taken into consideration when navigating across country.
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FM 3-25.26
Figure 5-7. Reading the extension scale.
i. The amount of time required to travel a certain distance on the ground is an important
factor in most military operations. This can be detennined if a map of the area is available
and a graphic time-distance scale is constructed for use with the map as follows:
R = Rate of travel (speed) T = Time
D = Distance (ground distance) T = D
R
For example, if an infantry unit is marching at an average rate (R) of 4 kilometers per hour,
it will take about 3 hours (T) to travel 12 kilometers.
12(D ) = 3 (T)
4(R)
j . To construct a time-distance scale (Figure 5-8A), knowing your length of march, rate
of speed, and map scale, that is, 12 kilometers at 3 kilometers per hour on a 1:50, 000-scale
map, use the following process:
(1) Mark off the total distance on a line by referring to the graphic scale of the map or,
if this is impracticable, compute the length of the line as follows:
(a) Convert the ground distance to centimeters: 12 kilometers x 100,000 (centimeters
per kilometer) = 1,200,000 centimeters.
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FM 3-25.26
(b) Find the length of the line to represent the distance at map scale —
MD = 1 = 1,200,000 = 24 centimeters
50,000 50,000
(c) Construct a line 24 centimeters in length (Figure 5-8A).
(2) Divide the line by the rate of march into three parts (Figure 5-8B), each part
representing the distance traveled in one hour, and label.
(3) Divide the scale extension (left portion) into the desired number of lesser time
divisions —
1-minute divisions — 60
5-minute divisions — 12
10-minute divisions — 6
(4) Figure 5-8C shows a 5 -minute interval scale. Make these divisions in the same
manner as for a graphic scale. The completed scale makes it possible to detennine where the
unit will be at any given time. However, it must be remembered that this scale is for one
specific rate of march only, 4 kilometers per hour.
(Length of lines are illustrative only and not at f :50,000 scale)
24 CENTIMETERS
1 HOUR
1 HOUR
2 HOURS
I I I I
1 HOUR
1 HOUR 2 HOURS
24 centimeters (5-minute intervals)
(Rate of march: 4-kilometers per hour)
Figure 5-8. Constructing a time-distance scale.
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FM 3-25.26
5-3. OTHER METHODS
Determining distance is the most common source of error encountered while moving either
mounted or dismounted. There may be circumstances where you are unable to detennine
distance using your map or where you are without a map. It is therefore essential to learn
methods by which you can accurately pace, measure, use subtense, or estimate distances on
the ground.
a. Pace Count. Another way to measure ground distance is the pace count. A pace is
equal to one natural step, about 30 inches long. To accurately use the pace count method,
you must know how many paces it takes you to walk 100 meters. To detennine this, you
must walk an accurately measured course and count the number of paces you take. A pace
course can be as short as 100 meters or as long as 600 meters. The pace course, regardless
of length, must be on similar terrain to that you will be walking over. It does no good to walk
a course on flat terrain and then try to use that pace count on hilly tenain. To determine your
pace count on a 600-meter course, count the paces it takes you to walk the 600 meters, then
divide the total paces by 6. The answer will give you the average paces it takes you to walk
100 meters. It is important that each person who navigates while dismounted knows his pace
count.
(1) There are many methods to keep track of the distance traveled when using the pace
count. Some of these methods are: put a pebble in your pocket every time you have walked
100 meters according to your pace count; tie knots in a string; or put marks in a notebook.
Do not try to remember the count; always use one of these methods or design your own
method.
(2) Certain conditions affect your pace count in the field, and you must allow for them
by making adjustments.
(a) Slopes. Your pace lengthens on a downslope and shortens on an upgrade. Keeping
this in mind, if it normally takes you 120 paces to walk 100 meters, your pace count may
increase to 130 or more when walking up a slope.
(b) Winds. A head wind shortens the pace and a tail wind increases it.
(c) Surfaces. Sand, gravel, mud, snow, and similar surface materials tend to shorten the
pace.
(d) Elements. Falling snow, rain, or ice cause the pace to be reduced in length.
(e) Clothing. Excess clothing and boots with poor traction affect the pace length.
(f) Visibility. Poor visibility, such as in fog, rain, or darkness, will shorten your pace.
b. Odometer. Distances can be measured by an odometer, which is standard equipment
on most vehicles. Readings are recorded at the start and end of a course and the difference
is the length of the course.
(1) To convert kilometers to miles, multiply the number of kilometers by 0.62.
EXAMPLE:
16 kilometers = 16 x 0.62 = 9.92 miles
(2) To convert miles to kilometers, divided the number of miles by 0.62.
EXAMPLE:
10 miles = 10 divided by 0.62 = 16.12 kilometers
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FM 3-25.26
c. Subtense. The subtense method is a fast method of detennining distance and yields
accuracy equivalent to that obtained by measuring distance with a premeasured piece of
wire. An advantage is that a horizontal distance is obtained indirectly; that is, the distance
is computed rather than measured. This allows subtense to be used over terrain where
obstacles such as streams, ravines, or steep slopes may prohibit other methods of
determining distance.
(1) The principle used in detennining distance by the subtense method is similar to that
used in estimating distance by the mil relation formula. The field artillery application of the
mil relation formula involves only estimations. It is not accurate enough for survey purposes.
However, the subtense method uses precise values with a trigonometric solution. Subtense
is based on a principle of visual perspective — the farther away an object, the smaller it
appears.
(2) The following two procedures are involved in subtense measurement:
• Establishing a base of known length.
• Measuring the angle of that base by use of the aiming circle.
(3) The subtense base may be any desired length. However, if a 60-meter base, a 2-meter
bar, or the length of an M16A1 or M16A2 rifle is used, precomputed subtense tables are
available. The M16 or 2-meter bar must be held horizontal and perpendicular to the line of
sight by a soldier facing the aiming circle. The instrument operator sights on one end of the
M16 or 2-meter bar and measures the horizontal clockwise angle to the other end of the rifle
or bar. He does this twice and averages the angles. He then enters the appropriate subtense
table with the mean angle and extracts the distance. Accurate distances can be obtained with
the M16 out to approximately 150 meters, with the 2-meter bar out to 250 meters, and with
the 60-meter base out to 1,000 meters. If a base of another length is desired, a distance can
be computed by using the following fonnula:
Distance = 1/2 ( base in meters )
Tan (1/2) (in mils)
d. Estimation. At times, because of the tactical situation, it may be necessary to
estimate range. There are two methods that may be used to estimate range or distance.
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FM 3-25.26
(1) 100-Meter Unit-of-Measure Method. To use this method, the soldier must be able
to visualize a distance of 100 meters on the ground. For ranges up to 500 meters, he
determines the number of 100-meter increments between the two objects he wishes to
measure. Beyond 500 meters, the soldier must select a point halfway to the object(s) and
detennine the number of 100-meter increments to the halfway point, then double it to find
the range to the object(s) (Figure 5-9).
Figure 5-9. Using a 100-meter unit-of-measure method.
(2) Flash-To-Bang Method. To use this method to determine range to an explosion or
enemy fire, begin to count when you see the flash. Count the seconds until you hear the
weapon fire. This time interval may be measured with a stopwatch or by using a steady
count, such as one-thousand-one, one -thousand-two, and so forth, for a three-second
estimated count. If you must count higher than 10 seconds, start over with one. Multiply the
number of seconds by 330 meters to get the approximate range (FA uses 350 meters instead).
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FM 3-25.26
(3) Proficiency of Methods. The methods discussed above are used only to estimate
range (Table 5-1). Proficiency in both methods requires constant practice. The best training
technique is to require the soldier to pace the range after he has estimated the distance. In
this way, the soldier discovers the actual range for himself, which makes a greater
impression than if he is simply told the correct range.
Factors Affecting
Range Estimation
Factors Causing
Underestimation of Range
Factors Causing
Overestimation of Range
The clearness of
outline and details
of the object.
When most of the object is visible and
offers a clear outline.
When only a small part of the object
can be seen or the object is small in
relation to its surroundings.
Nature of terrain or
position of the
observer.
When looking across a depression that
is mostly hidden from view.
When looking downward from high
ground.
When looking down a straight, open
road or along a railroad.
When looking over uniform surfaces like
water, snow, desert, or grain fields.
In bright light or when the sun is shining
from behind the observer.
When looking across a depression
that is totally visible.
When vision is confined, as in
streets, draws, or forest trails.
When looking from low ground
toward high ground.
In poor light, such as dawn and
dusk; in rain, snow, fog; or when
the sun is in the observer’s eyes.
Light and
atmosphere
When the object is in sharp contrast with
the background or is silhouetted
because of its size, shape, or color.
When seen in the clear air of high
altitudes.
When object blends into the
background or terrain.
Table 5-1. Factors of range estimation.
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FM 3-25.26
CHAPTER 6
DIRECTION
Being in the right place at the prescribed time is necessary to
successfully accomplish military missions. Direction plays an important role
in a soldier's everyday life. It can be expressed as right, left, straight ahead,
and so forth; but then the question arises, "To the right of what?" This
chapter defines the word azimuth and the three different norths. It explains
in detail how to determine the grid and the magnetic azimuths with the use
of the protractor and the compass. It explains the use of some field-expedient
methods to find directions, the declination diagram, and the conversion of
azimuths from grid to magnetic and vice versa. It also includes some
advanced aspects of map reading, such as in tersection, resection, modified
resection, and polar plots.
6-1. METHODS OF EXPRESSING DIRECTION
Military personnel need a way of expressing direction that is accurate, is adaptable to any
part of the world, and has a common unit of measure. Directions are expressed as units of
angular measure.
a. Degree. The most common unit of measure is the degree (°) with its subdivisions of
minutes (') and seconds (").
1 degree = 60 minutes.
1 minute = 60 seconds.
b. Mil. Another unit of measure, the mil (abbreviated ih), is used mainly in artillery,
tank, and mortar gunnery. The mil expresses the size of an angle formed when a circle is
divided into 6,400 angles, with the vertex of the angles at the center of the circle. A
relationship can be established between degrees and mils. A circle equals 6400 mils divided
by 360 degrees, or 17.78 mils per degree. To convert degrees to mils, multiply degrees by
17.78.
c. Grad. The grad is a metric unit of measure found on some foreign maps. There are
400 grads in a circle (a 90-degree right angle equals 100 grads). The grad is divided into
100 centesimal minutes (centigrads) and the minute into 100 centesimal seconds
(milligrads).
6-2. BASE LINES
In order to measure something, there must always be a starting point or zero measurement.
To express direction as a unit of angular measure, there must be a starting point or zero
measure and a point of reference These two points designate the base or reference line. There
are three base lines — true north, magnetic north, and grid north. The most commonly used
are magnetic and grid.
a. True North. A line from any point on the earth's surface to the north pole. All lines
of longitude are true north lines. True north is usually represented by a star (Figure 6-1, page
6 - 2 ).
b. Magnetic North. The direction to the north magnetic pole, as indicated by the north-
seeking needle of a magnetic instrument. The magnetic north is usually symbolized by a line
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FM 3-25.26
ending with half of an arrowhead (Figure 6-1). Magnetic readings are obtained with
magnetic instruments, such as lensatic and M2 compasses.
c. Grid North. The north that is established by using the vertical grid lines on the map.
Grid north may be symbolized by the letters GN or the letter “y” (Figure 6-1).
6-3. AZIMUTHS
An azimuth is defined as a horizontal angle measured clockwise from a north base line. This
north base line could be true north, magnetic north, or grid north. The azimuth is the most
common military method to express direction. When using an azimuth, the point from which
the azimuth originates is the center of an imaginary circle (Figure 6-2). This circle is divided
into 360 degrees or 6400 mils (Appendix G).
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FM 3-25.26
Figure 6-2. Origin of azimuth circle.
a. Back Azimuth. A back azimuth is the opposite direction of an azimuth. It is
comparable to doing “about face.” To obtain a back azimuth from an azimuth, add
180 degrees if the azimuth is 180 degrees or less, or subtract 180 degrees if the azimuth is
180 degrees or more (Figure 6-3). The back azimuth of 180 degrees may be stated as
0 degrees or 360 degrees. For mils, if the azimuth is less than 3200 mils, add 3200 mils, if
the azimuth is more than 3200 mils, subtract 3200 mils.
Figure 6-3. Back azimuth.
WARNING
When converting azimuths into back azimuths, extreme care should be
exercised when adding or subtracting the 180 degrees. A simple
mathematical mistake could cause disastrous consequences.
b. Magnetic Azimuth. The magnetic azimuth is determined by using magnetic
instruments, such as lensatic and M2 compasses. Refer to Chapter 9, paragraph 4, for details.
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FM 3-25.26
c. Field-Expedient Methods. Several field-expedient methods to detennine direction
are discussed in Chapter 9, paragraph 5.
6-4. GRID AZIMUTHS
When an azimuth is plotted on a map between point A (starting point) and point B (ending
point), the points are joined together by a straight line. A protractor is used to measure the
angle between grid north and the drawn line, and this measured azimuth is the grid azimuth
(Figure 6-4).
WARNING
When measuring azimuths on a map, remember that you are measuring
from a starting point to an ending point. If a mistake is made and the
reading is taken from the ending point, the grid azimuth will be opposite,
thus causing the user to go in the wrong direction.
FM 3-25.26
Figure 6-4. Measuring an azimuth.
6-5. PROTRACTOR
There are several types of protractors — full circle, half circle, square, and rectangular
(Figure 6-5). All of them divide the circle into units of angular measure, and each has a scale
around the outer edge and an index mark. The index mark is the center of the protractor
circle from which all directions are measured.
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FM 3-25.26
Figure 6-5. Types of protractors.
a. The military protractor, GTA 5-2-12, contains two scales: one in degrees (inner
scale) and one in mils (outer scale). This protractor represents the azimuth circle. The degree
scale is graduated from 0 to 360 degrees; each tick mark on the degree scale represents one
degree. A line from 0 to 180 degrees is called the base line of the protractor. Where the base
line intersects the horizontal line, between 90 and 270 degrees, is the index or center of the
protractor (Figure 6-6).
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FM 3-25.26
b. When using the protractor, the base line is always oriented parallel to a north-south
grid line. The 0- or 360-degree mark is always toward the top or north on the map and the
90° mark is to the right.
(1) To determine the grid azimuth —
(a) Draw a line connecting the two points (A and B).
(b) Place the index of the protractor at the point where the drawn line crosses a vertical
(north-south) grid line.
(c) Keeping the index at this point, align the 0- to 1 80-degree line of the protractor on
the vertical grid line.
(d) Read the value of the angle from the scale; this is the grid azimuth from point A to
point B (Figure 6-4).
(2) To plot an azimuth from a kn own point on a map (Figure 6-7) —
(a) Convert the azimuth from magnetic to grid, if necessary. (See paragraph 6-6.)
(b) Place the protractor on the map with the index mark at the center of mass of the
known point and the base line parallel to a north-south grid line.
(c) Make a mark on the map at the desired azimuth.
(d) Remove the protractor and draw a line connecting the known point and the mark on
the map. This is the grid direction line (azimuth).
NOTE: When measuring an azimuth, the reading is always to the nearest degree or
10 mils. Distance does not change an accurately measured azimuth.
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FM 3-25.26
Figure 6-7. Plotting an azimuth on the map.
c. To obtain an accurate reading with the protractor (to the nearest degree or 10 mils),
there are two techniques to check that the base line of the protractor is parallel to a north-
south grid line.
(1) Place the protractor index where the azimuth line cuts a north-south grid line,
aligning the base line of the protractor directly over the intersection of the azimuth line with
the north-south grid line. The user should be able to determine whether the initial azimuth
reading was correct.
(2) The user should re-read the azimuth between the azimuth and north-south grid line
to check the initial azimuth.
(3) Note that the protractor is cut at both the top and bottom by the same north-south grid
line. Count the number of degrees from the 0-degree mark at the top of the protractor to this
north-south grid line and then count the number of degrees from the 1 80-degree mark at the
bottom of the protractor to this same grid line. If the two counts are equal, the protractor is
properly aligned.
6-6. DECLINATION DIAGRAM
Declination is the angular difference between any two norths. If you have a map and a
compass, the one of most interest to you will be between magnetic and grid north. The
declination diagram (Figure 6-8) shows the angular relationship, represented by prongs,
among grid, magnetic, and true norths. While the relative positions of the prongs are correct,
they are seldom plotted to scale. Do not use the diagram to measure a numerical value. This
value will be written in the map margin (in both degrees and mils) beside the diagram.
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FM 3-25.26
a. Location. A declination diagram is a part of the infonnation in the lower margin on
most larger maps. On medium-scale maps, the declination infonnation is shown by a note
in the map margin.
b. Grid-Magnetic Angle. The G-M angle value is the angular size that exists between
grid north and magnetic north. It is an arc, indicated by a dashed line, that connects the grid-
north and magnetic -north prongs. This value is expressed to the nearest 1/2 degree, with mil
equivalents shown to the nearest 10 mils. The G-M angle is important to the map reader/land
navigator because azimuths translated between map and ground will be in error by the size
of the declination angle if not adjusted for it.
c. Grid Convergence. An arc indicated by a dashed line connects the prongs for true
north and grid north. The value of the angle for the center of the sheet is given to the nearest
full minute with its equivalent to the nearest mil. These data are shown in the form of a grid-
convergence note.
d. Conversion. There is an angular difference between the grid north and the magnetic
north. Since the location of magnetic north does not correspond exactly with the grid-north
lines on the maps, a conversion from magnetic to grid or vice versa is needed.
(1) With Notes. Simply refer to the conversion notes that appear in conjunction with the
diagram explaining the use of the G-M angle (Figure 6-8). One note provides instructions
for converting magnetic azimuth to grid azimuth; the other, for converting grid azimuth to
magnetic azimuth. The conversion (add or subtract) is governed by the direction of the
magnetic -north prong relative to that of the north-grid prong.
(2) Without Notes. In some cases, there are no declination conversion notes on the
margin of the map; it is necessary to convert from one type of declination to another. A
magnetic compass gives a magnetic azimuth; but in order to plot this line on a gridded map,
the magnetic azimuth value must be changed to grid azimuth. The declination diagram is
used for these conversions. A rule to remember when solving such problems is this:
No matter where the azimuth line points, the angle to it is always measured clockwise
from the reference direction (base line). With this in mind, the problem is solved by the
following steps:
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FM 3-25.26
(a) Draw a vertical or grid-north line (prong). Always align this line with the vertical
lines on a map (Figure 6-9).
Figure 6-9. Declination diagram with arbitrary line.
(b) From the base of the grid-north line (prong), draw an arbitrary line (or any azimuth
line) at a roughly right angle to north, regardless of the actual value of the azimuth in degrees
(Figure 6-9).
(c) Examine the declination diagram on the map and determine the direction of the
magnetic north (right-left or east-west) relative to that of the grid-north prong. Draw a
magnetic prong from the apex of the grid-north line in the desired direction (Figure 6-9).
(d) Determine the value of the G-M angle. Draw an arc from the grid prong to the
magnetic prong and place the value of the G-M angle (Figure 6-9).
(e) Complete the diagram by drawing an arc from each reference line to the arbitrary
line. A glance at the completed diagram shows whether the given azimuth or the desired
azimuth is greater, and thus whether the known difference between the two must be added
or subtracted.
(f) The inclusion of the true -north prong in relationship to the conversion is of little
importance.
e. Applications. Remember, there are no negative azimuths on the azimuth circle. Since
0 degree is the same as 360 degrees, then 2 degrees is the same as 362 degrees. This is
because 2 degrees and 362 degrees are located at the same point on the azimuth circle. The
grid azimuth can now be converted into a magnetic azimuth because the grid azimuth is now
larger than the G-M angle.
(1) When working with a map having an east G-M angle:
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FM 3-25.26
(a) To plot a magnetic azimuth on a map, first change it to a grid azimuth (Figure 6-10).
Figure 6-10. Converting to grid azimuth.
(b) To use a magnetic azimuth in the field with a compass, first change the grid azimuth
plotted on a map to a magnetic azimuth (Figure 6-11).
Figure 6-11. Converting to magnetic azimuth.
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FM 3-25.26
(c) Convert a grid azimuth to a magnetic azimuth when the G-M angle is greater than
a
grid azimuth (Figure 6-12).
Figure 6-12. Converting to a magnetic azimuth
when the G-M angle is greater.
(2) When working with a map having a west G-M angle:
(a) To plot a magnetic azimuth on a map, first convert it to a grid azimuth (Figure 6-13).
Figure 6-13. Converting to a grid azimuth on a map.
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FM 3-25.26
(b) To use a magnetic azimuth in the field with a compass, change the grid azimuth
plotted on a map to a magnetic azimuth (Figure 6-14).
Figure 6-14. Converting to a magnetic azimuth on a map.
(c) Convert a magnetic azimuth when the G-M angle is greater than the magnetic
azimuth (Figure 6-15).
Figure 6-15. Converting to a grid azimuth
when the G-M angle is greater.
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FM 3-25.26
(3) The G-M angle diagram should be constructed and used each time the conversion of
azimuth is required. Such procedure is important when working with a map for the first time.
It also may be convenient to construct a G-M angle conversion table on the margin of the
map.
NOTE: When converting azimuths, exercise extreme care when adding and subtracting
the G-M angle. A simple mistake of 1° could be significant in the field.
6-7. INTERSECTION
Intersection is the location of an unknown point by successively occupying at least two
(preferably three) known positions on the ground and then map sighting on the unknown
location. It is used to locate distant or inaccessible points or objects such as enemy targets
and danger areas. There are two methods of intersection: the map and compass method and
the straightedge method (Figures 6-16 and 6-17 on pages 6-14 and 6-15).
a. When using the map and compass method —
(1) Orient the map using the compass.
(2) Locate and mark your position on the map,
(3) Detennine the magnetic azimuth to the unknown position using the compass.
(4) Convert the magnetic azimuth to grid azimuth.
(5) Draw a line on the map from your position on this grid azimuth.
(6) Move to a second known point and repeat steps 1, 2, 3, 4, and 5.
(7) The location of the u nk nown position is where the lines cross on the map. Detennine
the grid coordinates to the desired accuracy.
b. The straight edge method is used when a compass is not available. When using it —
(1) Orient the map on a flat surface by the terrain association method.
(2) Locate and mark your position on the map.
(3) Lay a straight edge on the map with one end at the user’s position (A) as a pivot
point; then, rotate the straightedge until the unkown point is sighted along the edge.
(4) Draw a line along the straight edge
(5) Repeat the above steps at position (B) and check for accuracy.
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mmfr/M
Magnetic azimuth from position A 71 °+5° E =76°G
Magnetic azimuth from position B 35° +5° E =40°G
Figure 6-16. Intersection, using map and compass.
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(6) The intersection of the lines on the map is the location of the unknown point (C).
Determine the grid coordinates to the desired accuracy (Figure 6-17).
6-8. RESECTION
Resection is the method of locating one's position on a map by detennining the grid azimuth
to at least two well-defined locations that can be pinpointed on the map. For greater
accuracy, the desired method of resection would be to use three or more well-defined
locations.
a. When using the map and compass method (Figure 6-18) —
(1) Orient the map using the compass.
(2) Identify two or three known distant locations on the ground and mark them on the
map.
(3) Measure the magnetic azimuth to one of the known positions from your location
using a compass.
(4) Convert the magnetic azimuth to a grid azimuth.
(5) Convert the grid azimuth to a back azimuth. Using a protractor, draw a line for the
back azimuth on the map from the known position back toward your unknown position.
(6) Repeat 3, 4, and 5 for a second position and a third position, if desired.
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(7) The intersection of the lines is your location. Determine the grid coordinates to the
desired accuracy.
CONTROL TOWER
KNOWN DISTANT
LOCATION
1. From your unknown location to hilltop 408 magnetic azimuth
312° + 5° E = 317° G - 180° = 137° back azimuth
2. From your unknown location to control tower magnetic azimuth
13° + 5® E = 18°G + 180° = 198° back azimuth
esection with map and compass
-igure
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a. When using the straightedge method (Figure 6-19) —
(1) Orient the map on a flat surface by the terrain association method.
(2) Locate at least two known distant locations or prominent features on the ground and
mark them on the map.
(3) Lay a straightedge on the map using a known position as a pivot point. Rotate the
straightedge until the known position on the map is aligned with the known position on the
ground.
(4) Draw a line along the straightedge away from the known position on the ground
toward your position.
(5) Repeat 3 and 4 using a second known position.
(6) The intersection of the lines on the map is your location. Determine the grid
coordinates to the desired accuracy.
Figure 6-19. Resection with straightedge.
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6-9. MODIFIED RESECTION
Modified resection is the method of locating one's position on the map when the person is
located on a linear feature on the ground, such as a road, canal, or stream (Figure 6-20).
Proceed as follows:
a. Orient the map using a compass or by terrain association.
b. Find a distant point that can be identified on the ground and on the map.
c. Determine the magnetic azimuth from your location to the distant known point.
d. Convert the magnetic azimuth to a grid azimuth.
e. Convert the grid azimuth to a back azimuth. Using a protractor, draw a line for the
back azimuth on the map from the known position back toward your unknown position.
f. The location of the user is where the line crosses the linear feature. Determine the
grid coordinates to the desired accuracy.
YOUR UNKNOWN LOCATION
1. Your unknown location Is along Prairie Creek.
2. From your unknown location to the Church of God, the magnetic
azimuth la 20° + 7° E = 27° 0 + 1 80° = 207” back azimuth.
Figure 6-20. Modified resection.
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6-10. POLAR COORDINATES
A method of locating or plotting an unknown position from a known point by giving a
direction and a distance along that direction line is called polar coordinates. The following
elements must be present when using polar coordinates (Figure 6-21).
• Present known location on the map.
• Azimuth (grid or magnetic).
• Distance (in meters).
Figure 6-21. Polar plot.
Using the laser range finder to determine the range enhances your accuracy in detennining
the unknown position’s location.
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CHAPTER 7
OVERLAYS
An overlay is a clear sheet of plastic or semi-transparent paper. It is used
to display supplemental map and tactical information related to military
operations. It is often used as a supplement to orders given in the field.
Information is plotted on the overlay at the same scale as on the map, aerial
photograph, or other graphic being used. When the overlay is placed over
the graphic, the details plotted on the overlay are shown in their true
position.
7-1. PURPOSE
Overlays are used to display military operations with enemy and friendly troop dispositions,
and as supplements to orders sent to the field. They show detail that will aid in
understanding the orders, displays of communication networks, and so forth. They are also
used as annexes to reports made in the field because they can clarify matters that are difficult
to explain clearly in writing.
7-2. MAP OVERLAY
There are three steps in the making of a map overlay — orienting the overlay material,
plotting and symbolizing the detail, and adding the required marginal infonnation
(Figure 7-1).
Figure 7-1. Registering the overlay.
a. Orienting. Orient the overlay over the place on the map to be annotated. Then, if
possible, attach it to the edges of the map with tape. Trace the grid intersections nearest the
two opposite comers of the overlay using a straightedge and label each with the proper grid
coordinates. These register marks show the receiver of your overlay exactly where it fits on
his map; without them, the overlay is difficult to orient. It is imperative that absolute
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accuracy be maintained in plotting the register marks, as the smallest mistake will throw off
the overlay.
b. Plotting of New Detail. Use pencils or markers in standard colors that make a lasting
mark without cutting the overlay to plot any detail (FM 101-5-1).
(1) Use standard topographic or military symbols where possible. Nonstandard symbols
invented by the author must be identified in a legend on the overlay. Depending on the
conditions under which the overlay is made, it may be advisable to plot the positions first
on the map, then trace them onto the overlay. Since the overlay is to be used as a supplement
to orders or reports and the recipient will have an identical map, show only that detail with
which the report is directly concerned.
(2) If you have observed any topographic or cultural features that are not shown on the
map, such as a new road or a destroyed bridge, plot their positions as accurately as possible
on the overlay and mark with the standard topographic symbol.
(3) If difficulty in seeing through the overlay material is encountered while plotting or
tracing detail, lift the overlay from time to time to check orientation of information being
added in reference to the base.
c. Recording Marginal Information. When all required detail has been plotted or
traced on the overlay, print information as close to the lower right-hand comer as detail
pennits (Figure 7-2). This information includes the following data:
(1) Title and Objective. This tells the reader why the overlay was made and may also
give the actual location. For example, "Road Reconnaissance" is not as specific as "Route
146 Road Reconnaissance."
(2) Time and Date. Any overlay should contain the latest possible infonnation. An
overlay received in time is very valuable to the planning staff and may affect the entire
situation; an overlay that has been delayed for any reason may be of little use. Therefore, the
exact time the information was obtained aids the receivers in determining its reliability and
usefulness.
(3) Map Reference. The sheet name, sheet number, map series number, and scale must
be included. If the reader does not have the map used for the overlay, this provides the
information necessary to obtain it.
(4) Author. The name, rank, and organization of the author, supplemented with a date
and time of preparation of the overlay, tells the reader if there was a time difference between
when the infonnation was obtained and when it was reported.
(5) Legend. If it is necessary to invent nonstandard symbols to show the required
information, the legend must show what these symbols mean.
(6) Security Classification. This must correspond to the highest classification of either
the map or the information placed on the overlay. If the information and map are
unclassified, this will be so stated. The locations of the classification notes are shown in
Figure 7-2, and the notes will appear in both locations as shown.
(7) Additional Information. Any other information that amplifies the overlay will also
be included. Make it as brief as possible.
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Figure 7-2. Map overlay with marginal information.
7-3. AERIAL PHOTOGRAPH OVERLAY
Overlays of single aerial photographs are constructed and used in the same way as map
overlays. The steps followed are essentially the same, with the following exceptions:
a. Orienting of Overlay. The photograph normally does not have grid lines to be used
as register marks. The borders of the photograph limit the area of the overlay, so the
reference marks or linear features are traced in place of grid register marks. Finally, to ensure
proper location of the overlay with respect to the photograph, indicate on the overlay the
position of the marginal data on the photograph as seen through the overlay.
b. Marginal Information. The marginal infonnation shown on photographs varies
somewhat from that shown on maps. Overlays of photographs (Figure 7-3, page 7-4) should
show the following infonnation:
(1) North Arrow. This may be obtained in two ways — by comparing with a map of the
area or by orienting the photograph by inspection. In the latter case, a compass or expedient
direction finder must be used to place the direction arrow on the overlay. Use the standard
symbol to represent the actual north anow used — grid, magnetic, or true north.
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(2) Title and Objective. This tells the reader why the photo overlay was made and may
also give the actual location.
(3) Time and Date. The exact time the infonnation was obtained is shown on a photo
overlay just as on a map overlay
(4) Photo Reference. The photo number, mission number, date of flight, and scale
appear here, or the information is traced in its actual location on the photograph.
(5) Scale. The scale must be computed since it is not part of the marginal data.
(6) Map Reference. Reference is made to the sheet name, sheet number, series number,
and scale of a map of the area, if one is available.
(7) Author. The name, rank, and organization of the author are shown, supplemented
with a date and time of preparation of the overlay.
(8) Legend. As with map overlays, this is only necessary when nonstandard symbols are
used.
(9) Security Classification. This must correspond to the highest classification of either
the photograph or the infonnation placed on the overlay. If the information and photograph
are unclassified, this will be so stated. The locations of the classification notes are shown in
Figure 7-3, and the notes will appear in both locations.
(10) Additional Information. Any other information that amplifies the overlay will also
be included. Make it as brief as possible.
Figure 7-3. Photographic overlay with marginal information.
FM 3-25.26
CHAPTER 8
AERIAL PHOTOGRAPHS
An aerial photograph is any photograph taken from an airborne vehicle
(aircraft, drones, balloons, satellites, and so forth). The aerial photograph
has many uses in military operations; however, for the purpose of this
manual, it will be considered primarily as a map supplement or map
substitute.
8-1. COMPARISON WITH MAPS
A topographic map may be obsolete because it was compiled many years ago. A recent aerial
photograph shows any changes that have taken place since the map was made. For this
reason, maps and aerial photographs complement each other. More information can be
gained by using the two together than by using either alone.
a. Advantages. An aerial photograph has the following advantages over a map:
(1) It provides a current pictorial view of the ground that no map can equal.
(2) It is more readily obtained. The photograph may be in the hands of the user within
a few hours after it is taken; a map may take months to prepare.
(3) It may be made for places that are inaccessible to ground soldiers.
(4) It shows military features that do not appear on maps.
(5) It can provide a day-to-day comparison of selected areas, pennitting evaluations to
be made of enemy activity.
(6) It provides a pennanent and objective record of the day-to-day changes with the area.
b. Disadvantages. The aerial photograph has the following disadvantages as compared
to a map:
(1) Ground features are difficult to identify or interpret without symbols and are often
obscured by other ground detail as, for example, buildings in wooded areas.
(2) Position location and scale are only approximate.
(3) Detailed variations in the terrain features are not readily apparent without
overlapping photography and a stereoscopic viewing instrument.
(4) Because of a lack of contrasting colors and tone, a photograph is difficult to use in
poor light.
(5) It lacks marginal data.
(6) It requires more training to interpret than a map.
8-2. TYPES
Aerial photography most commonly used by military personnel may be divided into two
major types, the vertical and the oblique. Each type depends upon the attitude of the camera
with respect to the earth's surface when the photograph is taken.
a. Vertical. A vertical photograph is taken with the camera pointed as straight down
as possible (Figures 8-1 and 8-2 on page 8-2). Allowable tolerance is usually + 3° from the
perpendicular (plumb) line to the camera axis. The result is coincident with the camera axis.
A vertical photograph has the following characteristics:
(1) The lens axis is perpendicular to the surface of the earth.
(2) It covers a relatively small area.
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(3) The shape of the ground area covered on a single vertical photo closely approximates
a square or rectangle.
(4) Being a view from above, it gives an unfamiliar view of the ground.
(5) Distance and directions may approach the accuracy of maps if taken over flat terrain.
(6) Relief is not readily apparent.
Figure 8-1 . Relationship of the vertical aerial
photograph with the ground.
Figure 8-2. Vertical photograph.
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a. Low Oblique. This is a photograph taken with the camera inclined about 30° from
the vertical (Figure 8-3, and Figure 8-4 on page 8-4). It is used to study an area before an
attack, to substitute for a reconnaissance, to substitute for a map, or to supplement a map.
A low oblique has the following characteristics:
(1) It covers a relatively small area.
(2) The ground area covered is a trapezoid, although the photo is square or rectangular.
(3) The objects have a more familiar view, comparable to viewing from the top of a high
hill or tall building.
(4) No scale is applicable to the entire photograph, and distance cannot be measured.
Parallel lines on the ground are not parallel on this photograph; therefore, direction (azimuth)
cannot be measured.
(5) Relief is discernible but distorted.
(6) It does not show the horizon.
Figure 8-3. Relationship of low oblique photograph to the ground.
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Figure 8-4. Low oblique photograph.
c. High Oblique. The high oblique is a photograph taken with the camera inclined
about 60° from the vertical (Figures 8-5 and 8-6). It has a limited military application; it is
used primarily in the making of aeronautical charts. However, it may be the only
photography available. A high oblique has the following characteristics:
(1) It covers a very large area (not all usable).
(2) The ground area covered is a trapezoid, but the photograph is square or rectangular.
(3) The view varies from the very familiar to unfamiliar, depending on the height at
which the photograph is taken.
(4) Distances and directions are not measured on this photograph for the same reasons
that they are not measured on the low oblique.
(5) Relief may be quite discernible but distorted as in any oblique view. The relief is not
apparent in a high altitude, high oblique.
(6) The horizon is always visible.
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Figure 8-5. Relationship of high oblique photograph to the ground.
Figure 8-6. High oblique photograph.
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d. Trimetrogon. This is an assemblage of three photographs taken at the same time,
one vertical and two high obliques, in a direction at right angle to the line of flight. The
obliques, taken at an angle of 60° from the vertical, sidelap the vertical photography,
producing composites from horizon to horizon (Figure 8-7).
Figure 8-7. Relationship of cameras to ground for trimetrogon
photography (three cameras).
e. Multiple Lens Photography. These are composite photographs taken with one
camera having two or more lenses, or by two or more cameras. The photographs are
combinations of two, four, or eight obliques around a vertical. The obliques are rectified to
permit assembly as verticals on a common plane.
f. Convergent Photography. These are done with a single twin-lens, wide-angle
camera, or with two single-lens, wide-angle cameras coupled rigidly in the same mount so
that each camera axis converges when intentionally tilted a prescribed amount (usually 1 5
or 20°) from the vertical. Again, the cameras are exposed at the same time. For precision
mapping, the optical axes of the cameras are parallel to the line of flight, and for
reconnaissance photography, the camera axes are at high angles to the line of flight.
g. Panoramic. The development and increasing use of panoramic photography in aerial
reconnaissance has resulted from the need to cover in greater detail more and more areas of
the world.
(1) To cover the large areas involved, and to resolve the desired ground detail, present-
day reconnaissance systems must operate at extremely high-resolution levels. Unfortunately,
high-resolution levels and wide-angular coverage are basically contradicting requirements.
(2) A panoramic camera is a scanning type of camera that sweeps the terrain of interest
from side to side across the direction of flight. This permits the panoramic camera to record
a much wider area of ground than either frame or strip cameras. As in the case of the frame
cameras, continuous cover is obtained by properly spaced exposures timed to give sufficient
overlap between frames. Panoramic cameras are most advantageous for applications
requiring the resolution of small ground detail from high altitudes.
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8-3. TYPES OF FILM
Types of film generally used in aerial photography include panchromatic, infrared, and color.
Camouflage detection film is also available.
a. Panchromatic. This is the same type of film that is used in the average hand-held
small camera. It records the amount of light reflected from objects in tones of gray running
from white to black. Most aerial photography is taken with panchromatic film.
b. Infrared. This is a black-and-white film that is sensitive to infrared waves. It can be
used to detect artificial camouflage materials and to take photographs at night if there is a
source of infrared radiation.
c. Color. This film is the same as that used in the average hand-held camera. It is
limited in its use because of the time required to process it and its need for clear, sunny
weather.
d. Camouflage Detection. This film is a special type that records natural vegetation in
a reddish color. When artificial camouflage materials are photographed, they appear bluish
or purplish. The name of this film indicates its primary use.
8-4. NUMBERING AND TITLING INFORMATION
Each aerial photograph contains in its margin important infonnation for the photo user. The
arrangement, type, and amount of this infonnation is standardized; however, the rapid
development of cameras, film, and aeronautical technology since World War II has caused
numerous changes in the numbering and titling of aerial photographs. As a result, the photo
user may find that the marginal information on older photographs varies somewhat from the
standard current practice. With certain camera systems, some of the data are automatically
recorded on each exposure, while other systems require that all titling data be added to the
film after processing.
a. Standard titling data for aerial photography prepared for the use of the Department
of Defense are as follows. For reconnaissance and charting photography, items 2 through 14
and item 19 are lettered on the beginning and end of each roll of film. Items 1 through 9 and
item 19 are lettered on each exposure. For surveying and mapping photography, items 2
through 19 are lettered on the beginning and end of each roll of film, and items 1, 2, 3, 5, 6,
7, 8, 9, 13, and 19 are lettered on each exposure.
(1) Negative number.
(2) Camera position.
(3) Taking unit.
(4) Service.
(5) Sortie/mission number.
(6) Date (followed by a double hyphen [=]).
(7) Time group and zone letter (GMT).
(8) Focal length.
(9) Altitude.
(10) Kind of photography or imagery.
(11) Geographic coordinates.
(12) Descriptive title.
(13) Proj ect number and or name.
(14) Camera type and serial number.
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(15) Cone serial number (if any).
(16) Lens type and serial number.
(17) Magazine type and serial number.
( 1 8) Type of photographic fdter used.
(19) Security classification.
b. Automatically recorded data may differ somewhat in arrangement from the sequence
listed above, but the same infonnation is available to the photo user. A detailed explanation
of the titling items and the codes used to indicate them is found in TM 5-243.
8-5. SCALE DETERMINATION
Before a photograph can be used as a map supplement or substitute, it is necessary to know
its scale. On a map, the scale is printed as a representative fraction that expresses the ratio
of map distance to ground distance, For example: RF = MD
GD
On a photograph, the scale is also expressed as a ratio, but is the ratio of the photo distance
(PD) to ground distance. For example: RF= PD
GD
The approximate scale or average scale (RF) of a vertical aerial photograph is determined
by either of two methods; the comparison method or the focal length-flight altitude method.
a. Comparison Method. The scale of a vertical aerial photograph is detennined by
comparing the measured distance between two points on the photograph with the measured
ground distance between the same two points.
SCALE (RF = Photo Distance
Ground Distance
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The ground distance is determined by actual measurement on the ground or by the use of the
scale on a map of the same area. The points selected on the photograph must be identifiable
on the ground or map of the same area and should be spaced in such a manner that a line
connecting them will pass through or nearly through the center of the photograph
(Figure 8-8).
Figure 8-8. Selection of points for scale determination.
b. Focal Length-Flight Altitude Method. When the marginal information of a
photograph includes the focal length and the flight altitude, the scale of the photo is
detennined using the following formula (Figure 8-9).
Figure 8-9. Computation of scale from terrain level.
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When the ground elevation is at sea level, H becomes zero, and the formula is as shown in
Figure 8-10.
Figure 8-10. Basic computation of scale from sea level.
8-6. INDEXING
When aerial photos are taken of an area, it is convenient to have a record of the extent of
coverage of each photo. A map on which the area covered by each photo is outlined and
numbered or indexed to correspond to the photo is called an index map. There are two
methods of preparing index maps.
a. The four-comer method (Figures 8-11 and 8-12) requires location on the map of the
exact point corresponding to each comer of the photo. If a recognizable object such as a
house or road junction can be found exactly at one of the comers, this point may be used on
the map as the corner of the photo. If recognizable objects cannot be found at the comers,
then the edges of the photo should be outlined on the map by lining up two or more
identifiable objects along each edge; the points where the edges intersect should be the exact
corners of the photo. If the photo is not a perfect vertical, the area outlined on the map will
not be a perfect square or rectangle. After the four sides are drawn on the map, the number
of the photograph is written in the enclosed area for identification. This number should be
placed in the same corner as it is on the photo.
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Figure 8-11. Four-corner method (selection of points).
Figure 8-12. Plotting, using the four-corner method.
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b. The template method is used when a large number of photos are to be indexed, and
the exact area covered by each is not as important as approximate area and location. In this
case, a template (cardboard pattern or guide) is cut to fit the average area the photos cover
on the index map. It is used to outline the individual area covered by each photo. To
construct a template, find the average map dimensions covered by the photos to be indexed
as follows. Multiply the average length of the photos by the denominator of the average scale
of the photos; multiply this by the scale of the map. Do the same for the width of the photos.
This gives the average length and width of the area each photo covers on the map— or the size
to which the template should be cut (Figure 8-13).
Figure 8-13. Constructing a template.
c. To index the map, select the general area covered by the first photo and orient the
photo to the map. Place the template over the area on the map and adjust it until it covers the
area as completely and accurately as possible. Draw lines around the edges of the template.
Remove the rectangle and proceed to the next photo (Figure 8-14).
Figure 8-14. Indexing with a template.
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d. After all photos have been plotted, write on the map sufficient infonnation to identify
the mission or sortie. If more than one sortie is plotted on one map or overlay, use a different
color for each sortie.
e. In most cases, when a unit orders aerial photography, an index is included to give the
basic information. Instead of being annotated on a map of the area, it appears on an overlay
and is keyed to a map.
8-7. ORIENTING OF PHOTOGRAPH
Orienting the photograph is important because it is of very little value as a map supplement
or substitute if its location and direction are not known by the user.
a. If a map of the same area as the photograph is available, the photograph is oriented
to the map by comparing features common to both and then transferring a direction line from
the map to the photograph.
b. If no map is available, the shadows on a photograph may be used to get an
approximate true-north line. This method is not recommended in the torrid zone
(Figure 8-15).
Example:
This photograph was taken on 29
December 1985 at 14:15 in the
afternoon. The long shadows of the
towers are to the right of north.
By measuring back 35° with a
protractor, an approximate true-north
line will be found.
OF SHADOW LINE
Figure 8-15. Using shadows on a photograph to find north.
(1) North Temperate Zone. The sun moves from the east in the morning through south
at noon to west in the afternoon. Conversely, shadow fall varies from west through north to
east. Before noon, therefore, north is to the right of the direction of shadow fall; at noon,
north is the direction of shadow fall; and after noon, north is to the left of shadow fall. On an
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FM 3-25.26
average, the amount of variation in shadow fall per hour is 15 degrees. From marginal
information, detennine the number of hours from noon that the photo was taken and multiply
that number by 15°. With a protractor, measure an angle of that amount in the proper
direction (right to left) from a clear, distinct shadow, and north is obtained. For photographs
taken within three hours of noon, a reasonable accurate north direction can be obtained.
Beyond these limits, the 15° must be corrected, depending on time of year and latitude.
(2) South Temperate Zone. The sun moves from east through north at noon to west.
Shadows then vary from west through south to east. Before noon, south is to the left of
shadow fall; at noon, south is shadow fall; and after noon, south is to the right of shadow fall.
Proceed as in (1) above to detennine the direction of south.
c. On a photograph that can be oriented to the surrounding ground features by
inspection, a magnetic-north line can be established using a compass.
(1) Orient the photograph by inspection.
(2) Open the compass and place it on the photograph.
(3) Without moving the photograph, rotate the compass until the north arrow is under
the stationary black line.
(4) Draw a line along the straight edge of the compass. This is a magnetic-north line.
8-8. POINT DESIGNATION GRID
Since aerial photographs are seldom exactly the same scale as a map of the same area, it is
not feasible to print military grids on them. A special grid is used for the designation of
points on photographs (Figure 8-16). This grid, known as the point designation grid, has no
relation to the scale of the photo, to any direction, or to the grid used on any other
photograph or map. It has only one purpose, to designate points on photographs.
Figure 8-16. Point designation grid.
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a. The point designation grid is rarely printed on photographs; therefore, it becomes the
responsibility of each user to construct the grid on the photograph. All users must construct
the grid in exactly the same way. Before the grid can be constructed or used, the photograph
must be held so that the marginal information, regardless of where it is located, is in the
normal reading position (Figure 8-17, step 1).
(1) Draw lines across the photograph joining opposite reference marks at the center of
each photograph (fiducial marks). If there are no fiducial marks, the center of each side of
the photograph is assumed to be the location of the marks (Figure 8-17, step 2).
(2) Space grid lines, starting with the center line, 4 centimeters (1.575 inches) apart (a
distance equal to 1,000 meters at a scale of 1:25,000). The 1:25,000 map coordinate scale
can be used for this dimension and to accurately designate points on the photograph, but this
does not mean that distance can be scaled from the photograph. Extend the grid past the
margins of the photograph so that a horizontal and vertical grid line fall outside the picture
area (Figure 8-17, step 3).
(3) Number each center line "50" and give numerical values to the remaining horizontal
and vertical lines so that they increase to the right and up (Figure 8-17, step 4).
Figure 8-17. Constructing a point designation grid.
8-15
FM 3-25.26
b. The point designation grid is used, once the photograph is oriented, in the same
manner as the grid on a map (Figure 8-18), read right and up. The coordinate scale used
with the UTM grid on maps at the scale of 1 :25,000 may be used to subdivide the grid square
in the same manner as on a map. However, because the same point designation grid is used
on all photographs, the coordinates of a point on the photograph must be prefixed by the
identifying marginal information of the photograph.
53
52
51
50
49
48
47
FOURTH: Estimate tenths between line
and points
FTT-
L i_r
THIRD: Read number labeling this line
SECOND: Estimate tenths between
6 1-
line and point
FIRST: Read number labeling this line
m
REFERENCE:
MARQINAL
INFORMATION
PLUS 506514
47
48 49 50 51 52 53
Figure 8-18. Reading point designation grid coordinates.
8-16
FM 3-25.26
c. A grid coordinate using the point designation grid (Figure 8-19) consists of three
parts:
(1) The letters "PDG" to indicate an aerial photograph rather than a map grid coordinate.
(2) The mission and photo negative number to identify which photograph is being used.
(3) The six numerical digits to locate the actual point on the photograph.
Figure 8-19. Locating the grid coordinate on a point designation grid.
8-9. IDENTIFICATION OF PHOTOGRAPH FEATURES
The identification of features on a photograph is not difficult if the following facts are
remembered. The view that is presented by the aerial photograph is from above and, as a
result, objects do not look familiar. Objects that are greatly reduced in size appear distorted.
Most aerial photography is black and white, and all colors appear on the photograph in
shades of gray. Generally speaking, the darker the natural color, the darker it will appear on
the photograph.
a. The identification of features on aerial photographs depends upon a careful
application of five factors of recognition. No one factor will give a positive identification;
it requires the use of all five.
(1) Size. The size of unknown objects on a photograph, as detennined from the scale of
the photograph or a comparison with known objects of known size, gives a clue to their
identity. For example, in a built-up area the smaller buildings are usually dwellings, and the
larger buildings are commercial or community buildings.
(2) Shape (Pattern). Many features possess characteristic shapes that readily identify the
features. Man-made features appear as straight or smooth curved lines, while natural features
usually appear to be irregular. Some of the most prominent man-made features are highways,
railroads, bridges, canals, and buildings. Compare the regular shapes of these to the irregular
shapes of such natural features as streams and timber lines.
(3) Shadows. Shadows are very helpful in identifying features since they show the
familiar side view of the object. Some excellent examples are the shadows of water towers
or smoke stacks. As viewed directly from above, only a round circle or dot is seen, whereas
the shadow shows the profile and helps to identify the object. Relative lengths of shadows
also usually give a good indication of relative heights of objects.
(4) Shade (Tone or Texture). Of the many different types of photographic film in use
today, the film used for most aerial photography, except for special purposes, is
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FM 3-25.26
panchromatic film. Panchromatic film is sensitive to all the colors of the spectrum; it
registers them as shades of gray, ranging from white to black. This lighter or darker shade
of features on aerial photographs is known as the tone. The tone is also dependent on the
texture of the features; a paved highway has a smooth texture and produces an even tone on
the photograph, while a recently plowed field or a marsh has a rough, choppy texture and
results in a rough or grainy tone. It is also important to remember that similar features may
have different tones on different photographs, depending on the reflection of sunlight. For
example, a river or body of water appears light if it is reflecting sunlight directly toward the
camera, but appears dark otherwise. Its texture may be smooth or rough, depending on the
surface of the water itself. As long as the variables are kept in mind, tone and texture may
be used to great advantage.
(5) Surrounding Objects. Quite often an object not easily recognized by itself may be
identified by its relative position to surrounding objects. Large buildings located beside
railroads or railroad sidings are usually factories or warehouses. Identify schools by the
baseball or football fields. It would be hard to tell the difference between a water tower next
to a railroad station and a silo next to a barn, unless the surrounding objects such as the
railroad tracks or cultivated fields were considered.
b. Before a vertical photograph can be studied or used for identification of features, it
must be oriented. This orienting is different from the orienting required for the construction
or use of the point designation grid. Orienting for study consists of rotating the photograph
so that the shadows on the photograph point toward yourself. You then face a source of light.
This places the source of light, an object, and its shadow in a natural relationship. Failure to
orient a photograph properly may cause the height or depth of an object to appear reversed.
For example, a mine or quarry may appear to be a hill instead of a depression.
8-10. STEREOVISION
One of the limitations of the vertical aerial photograph is the lack of apparent relief.
Stereoscopic vision (or as it is more commonly known, stereovision or depth perception) is
the ability to see three-dimensionally or to see length, width, and depth (distance) at the
same time. This requires two views of a single object from two slightly different positions.
Most people have the ability to see three-dimensionally. Whenever an object is viewed, it
is seen twice— once with the left eye and once with the right eye. The fusion or blending
together of these two images in the brain permits the judgment of depth or distance.
a. In taking aerial photographs, it is rare for only a single picture to be taken. Generally,
the aircraft flies over the area to be photographed taking a series of pictures, each of which
overlaps the photograph preceding it and the photograph following it so that an unbroken
coverage of the area is obtained (Figure 8-20). The amount of overlap is usually 56 percent,
which means that 56 percent of the ground detail appearing on one photo also appears on the
next photograph. When a single flight does not give the necessary coverage of an area,
additional flights must be made. These additional flights are parallel to the first and must
have an overlap between them. This overlap between flights is known as side lap and usually
is between 15 and 20 percent (Figure 8-21, page 8-20).
8-18
OVERLAP
Figure 8-20. Photographic overlap.
FM 3-25.26
Figure 8-21. Side lap.
ADJACENT PARALLEL FLIGHTS
b. The requirement for stereovision can be satisfied by overlapping photographs if one
eye sees the object on one photograph and the other eye sees the same object on another
photograph. While this can be done after practice with the eyes alone, it is much easier if an
optical aid is used. These optical aids are known as stereoscopes. There are many types of
stereoscopes, but only the two most commonly used are discussed in this manual.
(1) Pocket Stereoscope. The pocket stereoscope (Figure 8-22), sometimes known as a
lens stereoscope, consists of two magnifying lenses mounted in a metal frame. Because of
its simplicity and ease of carrying, it is the type used most frequently by military personnel.
8-20
FM 3-25.26
Figure 8-22. Pocket stereoscope.
(2) Mirror Stereoscope. The mirror stereoscope (Figure 8-23) is larger, heavier, and
more subject to damage than the pocket stereoscope. It consists of four mirrors mounted in
a metal frame.
Figure 8-23. Mirror stereoscope.
c. A method to orient a pair of aerial photographs for best three-dimensional viewing
is outlined below:
(1) Arrange the selected pair of photos in such a way that the shadows on them generally
appear to fall toward the viewer. It is also desirable that the light source enters the side away
from the observer during the study of the photographs (Figure 8-24, page 8-22).
(2) Place the pair of photographs on a flat surface so that the detail on one photograph
is directly over the same detail on the other photograph (Figure 8-24, page 8-22).
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FM 3-25.26
(3) Place the stereoscope over the photographs so that the left lens is over the left
photograph and the right lens is over the right photograph (Figure 8-24).
Figure 8-24. Placement of stereoscope over stereopair.
(4) Separate the photographs along the line of flight until a piece of detail appearing in
the overlap area of the left photograph is directly under the left lens and the same piece of
detail on the right photo is directly under the right lens.
(5) With the photograph and stereoscope in this position, a three-dimensional image
should be seen. A few minor adjustments may be necessary, such as adjusting the aerial
photographs of the stereoscope to obtain the correct position for your eyes. The hills appear
to rise and the valleys sink so that there is the impression of being in an aircraft looking
down at the ground.
(6) The identification of features on photographs is much easier and more accurate with
this three-dimensional view. The same five factors of recognition (size, shape, shadow, tone,
and surrounding objects) must still be applied; but now, with the addition of relief, a more
natural view is seen.
8-22
FM 3-25.26
PART TWO
LAND NAVIGATION
CHAPTER 9
NAVIGATION EQUIPMENT AND METHODS
Compasses are the primary navigation tools to use when moving in an
outdoor world where there is no other way to find directions. Soldiers should
be thoroughly familiar with the compass and its uses. Part One of this
manual discussed the techniques of map reading. To complement these
techniques, a mastery of field movement techniques is essential. This chapter
describes the lensatic compass and its uses, and some of the field expedient
methods used to find directions when compasses are not available.
9-1. TYPES OF COMPASSES
The lensatic compass is the most common and simplest instrument for measuring direction.
It is discussed in detail in paragraph 9-2. The artillery M2 compass is a special-purpose
instrument designed for accuracy; it will be discussed in Appendix G. The wrist/pocket
compass is a small magnetic compass that can be attached to a wristwatch band. It contains
a north-seeking arrow and a dial in degrees. A protractor can be used to detennine azimuths
when a compass is not available. However, it should be noted that when using the protractor
on a map, only grid azimuths are obtained.
9-2. LENSATIC COMPASS
The lensatic compass (Figure 9-1) consists of three major parts: the cover, the base, and the
lens.
LUMINOUS
SIGHTING DOTS
LUMINOUS MAGNETIC ARROW
SHORT LUMINOUS UNE
FIXED INDEX LINE
SIGHTING SLOT
LENS OR
REAR SIGHT
THUMB LOOP
FLOATING DIAL
BEZEL RING
COVER
BASE
Figure 9-1. Lensatic compass.
9-1
FM 3-25.26
a. Cover. The compass cover protects the floating dial. It contains the sighting wire
(front sight) and two luminous sighting slots or dots used for night navigation.
b. Base. The body of the compass contains the following movable parts:
(1) The floating dial is mounted on a pivot so it can rotate freely when the compass is
held level. Printed on the dial in luminous figures are an arrow and the letters E and W. The
arrow always points to magnetic north and the letters fall at east (E) 90° and west (W) 270°
on the dial. There are two scales; the outer scale denotes mils and the inner scale (normally
in red) denotes degrees.
(2) Encasing the floating dial is a glass containing a fixed black index line.
(3) The bezel ring is a ratchet device that clicks when turned. It contains 120 clicks when
rotated fully; each click is equal to 3°. A short luminous line that is used in conjunction with
the north-seeking arrow during navigation is contained in the glass face of the bezel ring.
(4) The thumb loop is attached to the base of the compass.
c. Lens. The lens is used to read the dial, and it contains the rear-sight slot used in
conjunction with the front for sighting on objects. The rear sight also serves as a lock and
clamps the dial when closed for its protection. The rear sight must be opened more than 45°
to allow the dial to float freely.
NOTE: When opened, the straightedge on the left side of the compass has a coordinate
scale; the scale is 1:50,000 in newer compasses.
WARNING
Some older compasses will have a 1:25,000 scale. This scale can be used
with a 1:50, 000-scale map, but the values read must be halved. Check the
scale.
9-3. COMPASS HANDLING
Compasses are delicate instruments and should be cared for accordingly.
a. Inspection. A detailed inspection is required when first obtaining and using a
compass. One of the most important parts to check is the floating dial, which contains the
magnetic needle. The user must also make sure the sighting wire is straight, the glass and
crystal parts are not broken, the numbers on the dial are readable, and most important, that
the dial does not stick.
b. Effects of Metal and Electricity. Metal objects and electrical sources can affect the
perfonnance of a compass. However, nonmagnetic metals and alloys do not affect compass
readings. The following separation distances are suggested to ensure proper functioning of
a compass:
High-tension power lines 55 meters.
Field gun, truck, or tank 18 meters.
Telegraph or telephone wires and barbed wire 10 meters.
Machine gun 2 meters.
Steel helmet or rifle 1/2 meter.
c. Accuracy. A compass in good working condition is very accurate. However, a
compass has to be checked periodically on a known line of direction, such as a surveyed
9-2
FM 3-25.26
azimuth using a declination station. Compasses with more than 3° + variation should not be
used.
d. Protection. If traveling with the compass unfolded, make sure the rear sight is fully
folded down onto the bezel ring. This will lock the floating dial and prevent vibration, as
well as protect the crystal and rear sight from damage.
9-4. USING A COMPASS
Magnetic azimuths are determined with the use of magnetic instruments, such as lensatic and
M2 compasses. The techniques employed when using the lensatic compass are as follows:
a. Using the Centerhold Technique. First, open the compass to its fullest so that the
cover fonns a straightedge with the base. Move the lens (rear sight) to the reannost position,
allowing the dial to float freely. Next, place your thumb through the thumb loop, form a
steady base with your third and fourth fingers, and extend your index finger along the side
of the compass. Place the thumb of the other hand between the lens (rear sight) and the bezel
ring; extend the index finger along the remaining side of the compass, and the remaining
fingers around the fingers of the other hand. Pull your elbows firmly into your sides; this will
place the compass between your chin and your belt. To measure an azimuth, simply turn
your entire body toward the object, pointing the compass cover directly at the object. Once
you are pointing at the object, look down and read the azimuth from beneath the fixed black
index line (Figure 9-2). This preferred method offers the following advantages over the
sighting technique:
(1) It is faster and easier to use.
(2) It can be used under all conditions of visibility.
(3) It can be used when navigating over any type of terrain.
(4) It can be used without putting down the rifle; however, the rifle must be slung well
back over either shoulder.
(5) It can be used without removing eyeglasses.
b. Using the Compass-to-Cheek Technique. Fold the cover of the compass containing
the sighting wire to a vertical position; then fold the rear sight slightly forward. Look
through the rear-sight slot and align the front-sight hairline with the desired object in the
distance. Then glance down at the dial through the eye lens to read the azimuth (Figure 9-3).
9-3
FM 3-25.26
NOTE: The compass-to-cheek technique is used almost exclusively for sighting, and it
is the best technique for this purpose.
c. Presetting a Compass and Following an Azimuth. Although different models of
the lensatic compass vary somewhat in the details of their use, the principles are the same.
(1) During daylight hours or with a light source:
(a) Hold the compass level in the palm of the hand.
(b) Rotate it until the desired azimuth falls under the fixed black index line (for example,
320°), maintaining the azimuth as prescribed (Figure 9-4).
(c) Turn the bezel ring until the luminous line is aligned with the north-seeking arrow.
Once the alignment is obtained, the compass is preset.
(d) To follow an azimuth, assume the centerhold technique and turn your body until the
north-seeking arrow is aligned with the luminous line. Then proceed forward in the direction
of the front cover's sighting wire, which is aligned with the fixed black index line that
contains the desired azimuth.
9-4
Figure 9-4. Compass preset at 320 degrees.
(2) During limited visibility, an azimuth may be set on the compass by the click method.
Remember that the bezel ring contains 3° intervals (clicks).
(a) Rotate the bezel ring until the luminous line is over the fixed black index line.
(b) Find the desired azimuth and divide it by three. The result is the number of clicks that
you have to rotate the bezel ring.
(c) Count the desired number of clicks. If the desired azimuth is smaller than 180°, the
number of clicks on the bezel ring should be counted in a counterclockwise direction. For
example, the desired azimuth is 51°. Desired azimuth is 51°-r 3 = 17 clicks
counterclockwise. If the desired azimuth is larger than 180°, subtract the number of degrees
from 360° and divide by 3 to obtain the number of clicks. Count them in a clockwise
direction. For example, the desired azimuth is 330°; 360°-330° = 30 -t-3 = 10 clicks
clockwise.
(d) With the compass preset as described above, assume a centerhold technique and
rotate your body until the north-seeking arrow is aligned with the luminous line on the bezel.
Then proceed forward in the direction of the front cover’s luminous dots, which are aligned
with the fixed black index line containing the azimuth.
(e) When the compass is to be used in darkness, an initial azimuth should be set while
light is still available, if possible. With the initial azimuth as a base, any other azimuth that
is a multiple of three can be established through the use of the clicking feature of the bezel
ring.
9-5
FM 3-25.26
NOTE: Sometimes the desired azimuth is not exactly divisible by three, causing an option
of rounding up or rounding down. If the azimuth is rounded up, this causes an
increase in the value of the azimuth, and the object is to be found on the left. If
the azimuth is rounded down, this causes a decrease in the value of the azimuth,
and the object is to be found on the right.
d. Bypassing an Obstacle. To bypass enemy positions or obstacles and still stay
oriented, detour around the obstacle by moving at right angles for specified distances.
(1) For example, while moving on an azimuth of 90° change your azimuth to 180° and
travel for 100 meters. Change your azimuth to 90°and travel for 150 meters. Change your
azimuth to 360°and travel for 100 meters. Then, change your azimuth to 90°and you are back
on your original azimuth line (Figure 9-5).
Figure 9-5. Bypassing an obstacle.
(2) Bypassing an unexpected obstacle at night is a fairly simple matter. To make a 90°
turn to the right, hold the compass in the centerhold technique; turn until the center of the
luminous letter E is under the luminous line ( do not move the bezel ring). To make a 90° turn
to the left, turn until the center of the luminous letter W is under the luminous line. This does
not require changing the compass setting (bezel ring), and it ensures accurate 90° turns.
e. Offset. A deliberate offset is a planned magnetic deviation to the right or left of an
azimuth to an objective. Use it when the objective is located along or in the vicinity of a
linear feature such as a road or stream. Because of errors in the compass or in map reading,
the linear feature may be reached without knowing whether the objective lies to the right or
left. A deliberate offset by a known number of degrees in a known direction compensates
for possible errors and ensures that upon reaching the linear feature, the user knows whether
to go right or left to reach the objective. Ten degrees is an adequate offset for most tactical
uses. Each degree offset moves the course about 18 meters to the right or left for each
1,000 meters traveled. For example, in Figure 9-6, the number of degrees offset is 10. If the
9-6
FM 3-25.26
distance traveled to "x" in 1,000 meters, then "x" is located about 180 meters to the right of
the objective.
Figure 9-6. Deliberate offset to the objective.
9-5. FIELD-EXPEDIENT METHODS
When a compass is not available, different techniques should be used to detennine the four
cardinal directions.
a. Shadow-Tip Method.
(1) This simple and accurate method of finding direction by the sun consists of four basic
steps (Figure 9-7).
9-7
FM 3-25.26
Step 1. Place a stick or branch into the ground at a level spot where a distinctive shadow
will be cast. Mark the shadow tip with a stone, twig, or other means. This first shadow mark
is always the west direction.
Step 2. Wait 10 to 15 minutes until the shadow tip moves a few inches. Mark the new
position of the shadow tip in the same way as the first.
Step 3. Draw a straight line through the two marks to obtain an approximate east-west
line.
Step 4. Standing with the first mark (west) to your left, the other directions are simple;
north is to the front, east is to the right, and south is behind you.
(2) A line drawn perpendicular to the east-west line at any point is the approximate
north-south line. If you are uncertain which direction is east and which is west, observe this
simple rule— the first shadow-tip mark is always in the west direction, everywhere on earth.
(3) The shadow-tip method can also be used as a shadow clock to find the approximate
time of day (Figure 9-7 on page 9-7).
(a) To find the time of day, move the stick to the intersection of the east- west line and
the north-south line, and set it vertically in the ground. The west part of the east- west line
indicates 0600 hours, and the east part is 1800 hours, anywhere on earth, because the basic
rule always applies.
(b) The north-south line now becomes the noon line. The shadow of the stick is an hour
hand in the shadow clock, and with it you can estimate the time using the noon line and the
6 o'clock line as your guides. Depending on your location and the season, the shadow may
move either clockwise or counterclockwise, but this does not alter your manner of reading
the shadow clock.
(c) The shadow clock is not a timepiece in the ordinary sense. It makes every day 12
unequal hours long, and always reads 0600 hours at sunrise and 1800 hours at sunset. The
shadow clock time is closest to conventional clock time at midday, but the spacing of the
other hours compared to conventional time varies somewhat with the locality and the date.
However, it does provide a satisfactory means of telling time in the absence of properly set
watches.
(d) The shadow-tip system is not intended for use in polar regions, which the Department
of Defense defines as being above 60° latitude in either hemisphere. Distressed persons in
these areas are advised to stay in one place so that search/rescue teams may easily find them.
The presence and location of all aircraft and ground parties in polar regions are reported to
and checked regularly by governmental or other agencies, and any need for help becomes
quickly known.
b. Watch Method.
(1) A watch can be used to detennine the approximate true north and true south. In the
north temperate zone only, the hour hand is pointed toward the sun. A south line can be
found midway between the hour hand and 1200 hours, standard time. If on daylight saving
time, the north-south line is found between the hour hand and 1300 hours. If there is any
doubt as to which end of the line is north, remember that the sun is in the east before noon
and in the west after noon.
(2) The watch may also be used to determine direction in the south temperate zone;
however, the method is different. The 1200-hour dial is pointed toward the sun, and halfway
9-8
FM 3-25.26
between 1200 hours and the hour hand will be a north line. If on daylight saving time, the
north line lies midway between the hour hand and 1300 hours (Figure 9-8).
(3) The watch method can be in error, especially in the lower latitudes, and may cause
circling. To avoid this, make a shadow clock and set your watch to the time indicated. After
traveling for an hour, take another shadow-clock reading. Reset your watch if necessary.
c. Star Method.
(1) Less than 60 of approximately 5,000 stars visible to the eye are used by navigators.
The stars seen as we look up at the sky at night are not evenly scattered across the whole sky.
Instead they are in groups called constellations.
(2) The constellations that we see depends partly on where we are located on the earth,
the time of the year, and the time of the night. The night changes with the seasons because
of the journey of the earth around the sun, and it also changes from hour to hour because the
turning of the earth makes some constellations seem to travel in a circle. But there is one star
that is in almost exactly the same place in the sky all night long every night. It is the North
Star, also kn own as the Polar Star or Polaris.
(3) The North Star is less than 1° off true north and does not move from its place because
the axis of the earth is pointed toward it. The North Star is in the group of stars called the
Little Dipper. It is the last star in the handle of the dipper. There are two stars in the Big
Dipper, which are a big help when trying to find the North Star. They are called the Pointers,
and an imaginary line drawn through them five times their distance points to the North Star.
There are many stars brighter than the North Star, but none is more important because of its
location. However, the North Star can only be seen in the northern hemisphere so it cannot
serve as a guide south of the equator. The farther one goes north, the higher the North Star
is in the sky, and above latitude 70°, it is too high in the sky to be useful (Figure 9-9).
NORTH
SOUTH TEMPERATE
ZONE
Figure 9-8. Determining direction by using a watch.
9-9
FM 3-25.26
Figure 9-9. Determining direction by the
North Star and Southern Cross.
(4) Depending on the star selected for navigation, azimuth checks are necessary. A star
near the north horizon serves for about half an hour. When moving south, azimuth checks
should be made every 15 minutes. When traveling east or west, the difficulty of staying on
azimuth is caused more by the likelihood of the star climbing too high in the sky or losing
itself behind the western horizon than it is by the star changing direction angle. When this
happens, it is necessary to change to another guide star. The Southern Cross is the main
constellation used as a guide south of the equator, and the above general directions for using
north and south stars are reversed. When navigating using the stars as guides, the user must
know the different constellation shapes and their locations throughout the world (Figure 9-10
and Figure 9-11 on page 9-12).
9-10
FM 3-25.26
Figure 9-10. Constellations, northern hemisphere.
9-11
FM 3-25.26
APRIL
AQUARIUS
tINUS
FORNAX
(MICROSCOPIUM
ERIDANUS
GRUS
'SAGITTARII
TUCANA
'RETICULl
COffoNA
AUSTRALIS,
HYDRU!
LEPUS
kQfLLANIC
CtaOUD 0<
•mensa
JERPENS
CAUDA •
ORION
COLUMBA
CAN!S*1AJ<
>RPIUS
:ircinus*
OPNIUCHUS
CENTAURU!
HYDRA
CORVUS
CRATER
VIRGO
Figure 9-11. Constellations, southern hemisphere.
9-6. GLOBAL POSITIONING SYSTEM
The GPS is a space-based, global, all-weather, continuously available, radio positioning
navigation system. It is highly accurate in determining position location derived from signal
triangulation from a satellite constellation system. It is capable of determining latitude,
longitude, and altitude of the individual user. It is being fielded in hand-held, manpack,
vehicular, aircraft, and watercraft configurations. The GPS receives and processes data from
satellites on either a simultaneous or sequential basis. It measures the velocity and range
with respect to each satellite, processes the data in tenns of an earth-centered, earth-fixed
coordinate system, and displays the information to the user in geographic or military grid
coordinates.
a. The GPS can provide precise steering information, as well as position location. The
receiver can accept many checkpoints entered in any coordinate system by the user and
convert them to the desired coordinate system. The user then calls up the desired checkpoint
and the receiver will display direction and distance to the checkpoint. The GPS does not
9-12
FM 3-25.26
have inherent drift, an improvement over the Inertial Navigation System, and the receiver
will automatically update its position. The receiver can also compute time to the next
checkpoint.
b. Specific uses for the GPS are position location; navigation; weapon location; target
and sensor location; coordination of firepower; scout and screening operations; combat
resupply; location of obstacles, barriers, and gaps; and communication support. The GPS
also has the potential to allow units to train their soldiers and provide the following:
• Perfonnance feedback.
• Knowledge of routes taken by the soldier.
• Knowledge of errors committed by the soldier.
• Comparison of planned versus executed routes.
• Safety and control of lost and injured soldiers.
(See Appendix J for more infonnation of the GPS.)
9-13
FM 3-25.26
CHAPTER 10
ELEVATION AND RELIEF
The elevation of points on the ground and the relief of an area affect the
movement, positioning, and, in some cases, effectiveness of military units.
Soldiers must know how to determine locations of points on a map, measure
distances and azimuths, and identify symbols on a map. They must also be
able to determine the elevation and relief of areas on standard military maps.
To do this, they must first understand how the mapmaker indicated the
elevation and relief on the map.
10-1. DEFINITIONS
The reference or start point for vertical measurement of elevation on a standard military map
are the datum plane or mean sea level, the point halfway between high tide and low tide.
Elevation of a point on the earth’s surface is the vertical distance it is above or below mean
sea level. Relief is the representation (as depicted by the mapmaker) of the shapes of hills,
valleys, streams, or terrain features on the earth's surface.
10-2. METHODS OF DEPICTING RELIEF
Mapmakers use several methods to depict relief of the terrain.
a. Layer Tinting. Layer tinting is a method of showing relief by color. A different
color is used for each band of elevation. Each shade of color, or band, represents a definite
elevation range. A legend is printed on the map margin to indicate the elevation range
represented by each color. However, this method does not allow the map user to detennine
the exact elevation of a specific point — only the range.
b. Form Lines. Form lines are not measured from any datum plane. Form lines have
no standard elevation and give only a general idea of relief. Form lines are represented on
a map as dashed lines and are never labeled with representative elevations.
c. Shaded Relief. Relief shading indicates relief by a shadow effect achieved by tone
and color that results in the darkening of one side of terrain features, such as hills and ridges.
The darker the shading, the steeper the slope. Shaded relief is sometimes used in conjunction
with contour lines to emphasize these features.
d. Hachures. Hachures are short, broken lines used to show relief. Hachures are
sometimes used with contour lines. They do not represent exact elevations, but are mainly
used to show large, rocky outcrop areas. Hachures are used extensively on small-scale maps
to show mountain ranges, plateaus, and mountain peaks.
e. Contour Lines. Contour lines are the most common method of showing relief and
elevation on a standard topographic map. A contour line represents an imaginary line on the
ground, above or below sea level. All points on the contour line are at the same elevation.
The elevation represented by contour lines is the vertical distance above or below sea level.
The three types of contour lines (Figure 10-1, page 10-2) used on a standard topographic
map are as follows:
(1) Index. Starting at zero elevation or mean sea level, every fifth contour line is a
heavier line. These are known as index contour lines. Normally, each index contour line is
numbered at some point. This number is the elevation of that line.
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(2) Intermediate. The contour lines falling between the index contour lines are called
intennediate contour lines. These lines are finer and do not have their elevations given.
There are normally four intermediate contour lines between index contour lines.
(3) Supplementary. These contour lines resemble dashes. They show changes in
elevation of at least one-half the contour interval. These lines are normally found where there
is very little change in elevation, such as on fairly level terrain.
10-3. CONTOUR INTERVALS
Before the elevation of any point on the map can be determined, the user must know the
contour interval for the map he is using. The contour interval measurement given in the
marginal information is the vertical distance between adjacent contour lines. To determine
the elevation of a point on the map —
a. Determine the contour interval and the unit of measure used, for example, feet,
meters, or yards (Figure 10-2).
Figure 10-1. Contour lines.
ELEVATION IN METERS
CONTOUR INTERVAL 20 METERS
Figure 10-2. Contour interval note.
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b. Find the numbered index contour line nearest the point of which you are trying to
determine the elevation (Figure 10-3).
c. Determine if you are going from lower elevation to higher, or vice versa. In
Figure 10-3, point (a) is between the index contour lines. The lower index contour line is
numbered 500, which means any point on that line is at an elevation of 500 meters above
mean sea level. The upper index contour line is numbered 600, or 600 meters. Going from
the lower to the upper index contour line shows an increase in elevation.
d. Determine the exact elevation of point (a), start at the index contour line numbered
500 and count the number of intermediate contour lines to point (a). Locate point (a) on the
second intermediate contour line above the 500-meter index contour line. The contour
interval is 20 meters (Figure 10-2), thus each one of the intermediate contour lines crossed
to get to point (a) adds 20 meters to the 500-meter index contour line. The elevation of point
(a) is 540 meters; the elevation has increased.
e. Determine the elevation of point (b). Go to the nearest index contour line. In this
case, it is the upper index contour line numbered 600. Locate point (b) on the intermediate
contour line immediately below the 600-meter index contour line. Below means downhill
or a lower elevation. Therefore, point (b) is located at an elevation of 580 meters.
Remember, if you are increasing elevation, add the contour interval to the nearest index
contour line. If you are decreasing elevation, subtract the contour interval from the nearest
index contour line.
f. Determine the elevation to a hilltop point (c). Add one-half the contour interval to
the elevation of the last contour line. In this example, the last contour line before the hilltop
is an index contour line numbered 600. Add one-half the contour interval, 10 meters, to the
index contour line. The elevation of the hilltop would be 610 meters.
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g. There may be times when you need to detennine the elevation of points to a greater
accuracy. To do this, you must determine how far between the two contour lines the point
lies. However, most military needs are satisfied by estimating the elevation of points
between contour lines (Figure 10-4).
Figure 10-4. Points between contour lines.
(1) If the point is less than one-fourth the distance between contour lines, the elevation
will be the same as the last contour line. In Figure 10-4, the elevation of point a will be
100 meters. To estimate the elevation of a point between one-fourth and three-fourths of the
distance between contour lines, add one -half the contour interval to the last contour line.
(2) Point b is one-half the distance between contour lines. The contour line immediately
below point b is at an elevation of 160 meters. The contour interval is 20 meters; thus
one-half the contour interval is 10 meters. In this case, add 10 meters to the last contour line
of 160 meters. The elevation of point b would be about 170 meters.
(3) A point located more than three-fourths of the distance between contour lines is
considered to be at the same elevation as the next contour line. Point c is located three-
fourths of the distance between contour lines. In Figure 10-4 , point c would be considered
to be at an elevation of 180 meters.
h. To estimate the elevation to the bottom of a depression, subtract one-half the contour
interval from the value of the lowest contour line before the depression. In Figure 10-5, the
lowest contour line before the depression is 240 meters in elevation. Thus, the elevation at
the edge of the depression is 240 meters. To determine the elevation at the bottom of the
depression, subtract one-half the contour interval. The contour interval for this example is
20 meters. Subtract 10 meters from the lowest contour line immediately before the
depression. The result is that the elevation at the bottom of the depression is 230 meters. The
tick marks on the contour line forming a depression always point to lower elevations.
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Figure 10-5. Depression.
i. In addition to the contour lines, bench marks and spot elevations are used to indicate
points of kn own elevations on the map.
(1) Bench marks, the more accurate of the two, are symbolized by a black X, such as X
BM 214. The 214 indicates that the center of the X is at an elevation of 2 14 units of measure
(feet, meters, or yards) above mean sea level. To determine the units of measure, refer to the
contour interval in the marginal information.
(2) Spot elevations are shown by a brown X and are usually located at road junctions and
on hilltops and other prominent terrain features. If the elevation is shown in black numerals,
it has been checked for accuracy; if it is in brown, it has not been checked.
NOTE: New maps are being printed using a dot instead of brown Xs.
10-4. TYPES OF SLOPES
Depending on the military mission, soldiers may need to detennine not only the height of
a hill, but the degree of the hill's slope as well. The rate of rise or fall of a terrain feature is
known as its slope. The speed at which equipment or personnel can move is affected by the
slope of the ground or terrain feature. This slope can be determined from the map by
studying the contour lines — the closer the contour lines, the steeper the slope; the farther
apart the contour lines, the gentler the slope. Four types of slopes that concern the military
are as follows:
a. Gentle. Contour lines showing a uniform, gentle slope will be evenly spaced and
wide apart (Figure 10-6, page 10-6). Considering relief only, a uniform, gentle slope allows
the defender to use grazing fire. The attacking force has to climb a slight incline.
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Figure 10-6. Uniform, gentle slope.
b. Steep. Contour lines showing a unifonn, steep slope on a map will be evenly spaced,
but close together. Remember, the closer the contour lines, the steeper the slope
(Figure 10-7). Considering relief only, a unifonn, steep slope allows the defender to use
grazing fire, and the attacking force has to negotiate a steep incline.
Figure 10-7. Uniform, steep slope.
c. Concave. Contour lines showing a concave slope on a map will be closely spaced
at the top of the terrain feature and widely spaced at the bottom (Figure 10-8, page 10-7).
Considering relief only, the defender at the top of the slope can observe the entire slope and
the terrain at the bottom, but he cannot use grazing fire. The attacker would have no cover
from the defender's observation of fire, and his climb would become more difficult as he got
farther up the slope.
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Figure 10-8. Concave slope.
d. Convex. Contour lines showing a convex slope on a map will be widely spaced at
the top and closely spaced at the bottom (Figure 10-9). Considering relief only, the defender
at the top of the convex slope can obtain a small distance of grazing fire, but he cannot
observe most of the slope or the terrain at the bottom. The attacker will have concealment
on most of the slope and an easier climb as he nears the top.
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10-5. PERCENTAGE OF SLOPE
The speed at which personnel and equipment can move up or down a hill is affected by the
slope of the ground and the limitations of the equipment. Because of this, a more exact way
of describing a slope is necessary.
a. Slope may be expressed in several ways, but all depend upon the comparison of
vertical distance (VD) to
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