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"Where were you when I laid the earth's foundations?
Tell me, if you know and understand.
Who settled its dimensions? Surely you should know.
Who stretched his measuring-line over it?
On what do its supporting pillars rest?
Who set its corner-stone in place...?"
-The Lord to Job

    In the first issue of this series I spent some time discussing GPS receivers. I mentioned that for safety, GPS should be backed up by a second navigation system. In this issue I'll discuss some of the basics of terrestrial navigation with compass and map—orientation—that most elementary second system. All other field navigation methods are built on a foundation of orientation.

Orientation, part 2
(Maps/Navigation #2, November 21, 1998)

    There are four important activities in navigation, whether nautical or terrestrial:
  1. finding where you are;
  2. finding where you want to be;
  3. representing trip information on a map or chart;
  4. going there.
    Let me pause for a moment to present some important definitions we'll use throughout this and subsequent articles:
bearing:
the direction from an observer to a landmark, expressed in angular units.
course, or line of bearing:
direction of travel, expressed in angular units.
fix:
a precise location on the earth's surface.
orientation:
finding your way with map and compass.
representative fraction (RF)
a numerical indication of the relationship between distances on the map and distances on the ground. On a map with an RF of 1/24,000, one inch on the map represents 24,000 inches (2,000 feet) on the ground.
    For centuries navigators measured their position on the earth with optical instruments like the sextant, and with mathematical formulas. They still do, but now they also use electronic instruments like LORAN, RADAR, and the GPS; those older methods are not as important as they were.
    Another method was and still is commonly used: deduced reckoning, also called "dead" or "ded" reckoning. I like the last term better; it seems more optimistic. a simple DR fix In this very simple system the navigator's position at sea or on land can be fixed by two or more magnetic compass bearings to recognizable landmarks and adjusted by compensating for estimated speed over the ground.
    The end result of all these location methods is a fix, an expression of the navigator's position. It might look like one of these:
Sextant and tables (DMS):
N35º06'25", W106º37'27"
GPS (DM.M):
N35º06.4', W106º37.4'
ded reckoning:
"Dog Rock bears 270º, Bare Light bears 195º."
    Your destination can be expressed in the same terms. Even without a map or chart, using only navigational instruments, you could reach your destination...probably. You'd have to use the "cut and try" method, which isn't very efficient; and you couldn't be sure of what you might encounter on your way between your start and end points. But you could do it.
    Navigation becomes much more interesting, and infinitely more practical when you solve activity (3): representing your trip information on a chart or map.

Maps and Charts
    "A map is a picture of a portion of the earth's surface, seen from above and drawn to scale." That's the sentence that started our high school Army ROTC map training. It was burned into our brains. I didn't get very good at orientation way back then. I guess I wasn't ready for it. But I wanted to learn it, and I had the foresight to obtain a copy of our textbook, Army FM 21-26 Map Reading, for use sometime in the distant future when I would be ready. I did a lot of navigation in the Navy, and some ded reckoning; but it was always with nautical charts, a different breed of cat. I still wasn't ready for orientation. I was finally ready about five years ago.

Map Features
    Every map has a few common features that are required if the map is to be really useful:
  • a uniform drawing scale, expressed as a "representative fraction" (RF);
  • grid coordinates that relate the map to a position on the earth;
  • a compass rose or declination diagram for aligning the map correctly with the earth;
  • symbols representing real objects and their locations on the earth;
  • contour lines that represent the shape of the terrain depicted by the map;
  • margin information like map name, date, the names of adjoining maps, distance scales, and other notes of importance.
RF The RF expresses the relative size of a map compared to the portion of the earth it represents. For example, on a map with an RF of 1/250,000, one inch represents 250,000 inches on the ground, about four statute miles. This is a pretty small scale; that is, objects appear very small on the map.
    A common RF on maps used for detailed surveys or exploration is 1/24,000. One inch on this map represents 24,000 inches on the ground—2000 feet, about 3/8-mile. This large scale map depicts ground objects and distances with much greater resolution than small scale maps.
    A good selection of maps for hiking might include a 1/250,000 map of that large part of the state; a 1/100,000 map of the general hike area to show overall terrain features; and several adjoining 1/24,000 maps to show detail on the ground for the whole hike. A hiker might use the smaller scale maps to plan approaches and travel routes, the large scale maps to find certain objects on the ground. I also use a 1/500,000 map of each state I visit for finding cities, counties, parks, etc.
Map Grids Most people intuitively understand the purpose of a map grid—to divide the map into uniform rectangles in which to plot a location with good accuracy—sort of like a city street map with its streets and avenues.
    Two grid systems are in common use on American maps: the degree/minute/second (DMS) grid and the Universal Transverse Mercator (UTM) grid.
The DMS grid DMS grid system distances are based on the nautical mile, a unit of measure equal to one minute of latitude, or of longitude at the equator. This grid is very convenient for maritime navigators and aviators, but fairly difficult to use in terrestrial navigation.
    The grid "addresses" are based on angular distances (A) north and south of the equator (latitude) and (B) east and west of the 0º prime meridian (longitude), a line drawn from north pole to south pole through the Royal Observatory at Greenwich, England. Hey! Why not! You have to start somewhere, and the British got there first.
Earth and DMS Lat/Long DMS
DMS mirror fixes
DMS mirror fixes
    Most GPS receivers display locations in DMS (degrees, minutes, seconds) or DM.M (degrees/minutes/tenths of minutes), or both, which makes GPS locations a little easier to plot on DMS charts and maps.
    The DMS system is simple; using it is not. For example, distances are not represented uniformly on maps using the DMS system, since they are based on angles. Longitude angles farther from the equator encompass less linear distance. A simple (but not easy) way to solve this problem is to always use the distance scale or latitude coordinates to transfer map coordinates. For distances between points use the map distance scales. More about this later. Also, the modulo-60 DMS math is more difficult to use than ordinary decimal math
    Two other minor points, but ones that can lead to confusion—since the DMS system is based in the center of things (equator and prime meridian) locations are mirrored four ways. So what? There can be four locations on earth with the same numerical coordinates:
  1. N35º06'25", W106º37'27"
  2. N35º06'25", E106º37'27"
  3. S35º06'25", W106º37'27"
  4. S35º06'25", E106º37'27".
It's remarkably easy to write the wrong letters when you're in a hurry.
    Also, latitude angles must always be less than or equal to 90º, longitude angles less than or equal to 180º. For some people making errors like these can be fatal. It's no wonder that the U. S. Army doesn't use DMS in the field. Young soldiers with poor math background could get in lots of trouble.
The UTM Grid With 500 years of experience behind them, mapmakers finally developed a coordinate system that corrected most of the unwieldy characteristics of the DMS system. The UTM system divides the earth between latitude 80ºS and latitude 84ºN into sixty columns, or zones, each 6º wide. The zones are numbered from west to east, 1 through 60, starting at the 180º meridian.
earth and UTM UTM zone diagram 1

The rest of the earth, north and south of the UTM zones, is covered by the Universal Polar Stereographic grid (UPS).
    Any UTM zone can be identified by its unique number; a location within a zone by a unique pair of numbers. For example, Albuquerque, New Mexico, is located in zone 13, north of the equator, a very large place.
    UTM map grids are squares superimposed on the zones, beginning at the zone central meridian and at the equator. Distances are uniform. Depending on the map RF, the squares will be some decimal multiple of 1 km on a side.
    UTM "addresses" on the map grid are based on linear distances from the zone central meridian, which has been assigned a value of 500000 ; and north or south of the equator, which has been assigned a value of 0000000 for sites in the northern hemisphere, and 10000000 for sites in the southern hemisphere.
    "Doesn't that create mirror sites like the ones in the DMS system?" Yes, but only a pair for each zone. 120 mirror sites in all! Knowing the location's zone and it's position relative to the equator is a must.
    To solve the problem of mirror sites the U. S. military divided the zone columns into twenty rows 8º high. The rows are lettered "C" through "X" from south to north, starting at 80ºS latitude. The result is a grid of 6º x 8º rectangles, each with a unique, named location.
UTM mil. zone diagram

    The useful memory device "read right up" keeps us plotting in the right direction. Within the UTM zones, grid coordinates represent the distance from the zone central meridian and the equator. So, continuing with our example, with Albuquerque in zone 13, the junction of Interstate Highways 40 and 25 can be expressed in the UTM system only as:

13S     351986E     38 85925N.

    These peculiar numerical notations are typical of something from the système internationale (SI), or metric system, whose curators love to mess around with type fonts and goofy names. From the left, the first number is the UTM zone, the letter is the row designation. The next numbers, ending with the large digits, represent thousands, the right three digits represent units—all meters. So that Interstate junction is 351,986 meters right (east) of zone 13's central meridian, and 3,885,925 meters up (north) from the equator. For terrestrial navigators this system, though considerably more complex than the DMS or DM.M. systems, is much easier to use in the field, and that's what's important.

Grid Coordinates Maps are bordered by specified lines of latitude and longitude (DMS). It is common map maker practice to indicate intermediate parallels and meridians by tick marks printed along the map borders and within the map area. Grid lines are not usually projected across the map area. UTM grid tick marks are usually along the border, too, printed in blue.
Map tick marks

My 1953 map of Lake Poinsett, FL, is like that. I had to draw grid lines on that map by projecting them from the border tick marks. I used a sharp, hard lead pencil and a T-square for this tedious job. My 1983 map of Los Indios Canyon, NM, had UTM grid lines projected, but not DMS. Thirty years had made some changes in the methods of the USGS map makers, it seems.
    As convenient as printed grid lines are, the important thing is that both DMS and UTM tick marks and coordinates are present along the borders, and you can use them to accurately project map grid lines. DMS and UTM reference coordinates are identified in the map corners, so the tick marks are fairly easy to interpolate.
    Projecting grid lines and identifying them clearly before a trip saves a lot of confusion in the field. Wind and uneven terrain always make handling maps and thinking clearly harder.
    It is interesting that the two grids, DMS and UTM, are not necessarily congruent on the map. This is apparently because the UTM grid lines are artificial, superimposed on their zone grids by their own set of rules. Some grid line skew is almost always present.
Declination Diagram I have seen maps with full 360º compass rose overprinted, but only rarely. All nautical charts have them. The normal method of indicating north on a map is by declination diagram—a small graphic or notation in the lower map margin that shows any difference between true north and magnetic and grid norths. declination diagram
declination diagram
Three Norths? Time for three more definitions:
Grid north:
the bearing to the earth's actual north pole. It's parallel to the earth's prime meridian.
True north:
celestial north, the bearing to the earth's north pole as indicated by Polaris. Indicated by the N/S grid lines at the border of the map and the DMS tick marks along the map margins.
Magnetic north:
the bearing to the earth's magnetic north pole, indicated by magnetic compass after applying corrections for local magnetic errors and annual magnetic variations. Not gridded on maps.
    If a hiker intends to use a magnetic compass on his or her trip, magnetic north will be very important. Almost all GPS receivers display, or can be set to display, bearing and course as magnetic direction. As an old Navy man I initially believed true north would be more useful to me than magnetic. We used gyrocompasses to navigate onboard ship, and they read in true direction. I changed my mind after a little study and field practice. I now use magnetic north and do just fine.
    The magnetic error correction can be cranked in and marked on your map before your trip; but, for me, it's fairly easy to do in the field. I align my map with the declination diagram by simple math, without any difficult drawing. I'll show you my method later.

Caution:
the declination diagram is a representative graphic device, not an accurate angular representation. It is NOT OK to trust it as a direct alignment tool, no matter what your compass manufacturer says.

Map Symbols Important, prominent landmarks are printed on the map as symbols. They are seldom drawn to scale; their presence is intended to catch your eye as you compare the map to the terrain for recognizable features. If, for example, you see a windmill symbol on your map; a windmill bearing to your left, when you orient your map to magnetic north, may help you verify your position (ded reckoning again).
    Property lines, restricted area borders, roads, and trails are also represented as symbols and notes on the map.
    There are many map symbols in use. Most maps have at least a few of the most important ones included in a legend on the map or in its margin.
Contour Lines A map is a picture of a portion of the earth's surface as seen from above. Part of that view includes hills, valleys, flat areas, etc. You see these elevations with your two eyes as directly observable heights and depths. Maps must use a two-dimensional device—contour lines.
    Contour lines are usually printed in brown as continuous lines, marked in a regular progression of values of altitude above sea level. Peaks of hills are usually marked with a specific terminal value. Contour line intervals are elevation intervals, not horizontal distance intervals. Many contour lines spaced closely represent steep inclines; few, spaced far apart, represent gentler slopes.
map contours

Margin Information A great deal of useful information is printed in the map margin notes. Some of the most important information is:
  • the map name and number;
  • the map publication or revision date;
  • the RF;
  • the declination diagram;
  • map grid information (DMS or UTM);
  • grid coordinates;
  • distance scales;
  • symbol legend.
    Many large-scale maps identify adjoining maps in the series by printed names alongside the map borders and at the corners, or as a diagram in one of the margins. Since, for every map, there are eight adjoining maps, you can use this information before your trip to order maps of the surrounding areas, in case you hike completely off your main map.

Where to Obtain Maps
    High quality maps and charts are easy to obtain. Check with local book or map stores, engineering supply stores, and with mail order book and camping stores. The U. S. Geological Survey makes excellent maps of the U. S. in a variety of RFs, and sells them to the public at reasonable prices. Many commercial companies make excellent maps, too. We've listed a few links in our library, but you may find more in magazines oriented toward hiking, camping, or 4WD touring.

Locating Positions on A Map
    In the DMS and DM.M systems, distances are based on one minute of latitude and longitude. I use the old "one mile—one minute" memory aid to keep this in mind. Remember, though—that's one nautical mile—2020 yards, instead of 1760, as in a statute mile. Let's see how you can implement this third of the four basic navigation activities.
Marking Your Position With DMS To mark your position on the map, first find your position on the earth. You can use instruments, most likely the GPS receiver, to take a fix. You can either store the fix in the receiver memory or write it in your notebook. To mark the map you must have gridded it with lat/long lines projected accurately from the border tick marks at least into your travel area.
    To actually mark your position you'll have to determine the tick mark resolution (basic smallest interval) and interpolate to the resolution of your GPS fix. For example, a GPS fix in DMS notation:

N80º 20' 20", W106º 33' 10".

    First, locate your grid rectangle coarsely.
    Then (A) locate your vertical position by transferring the additional N distance from the map scale zone boundary to the grid lines. How? Subtract the map minute/second grid line coordinate from the fix minute/second coordinate:
fix 20' 20"
zone boundary -18' 00"
difference 2' 20"
2' 20" equals 2-1/3 nautical miles north of the south grid line.

Get vertical dimension
A. Mark latitude
    Finally, (B) locate your horizontal position from the map scale using the same method:
fix 33' 10"
zone boundary -33' 00"
difference 0' 10"
0' 10" equals 1/6 nautical mile (about 0.16 mile) west of the east grid line.
Final DMS position
B. Mark longitude
    It may or may not be apparent on your map that the DMS grid rectangles are not squares. This means that on the map a vertical minute is almost never the same size as a horizontal one. This adds a little to the complexity of the problem and to the accuracy of the solution. Just be sure you use the latitude scale to mark the latitude and longitude offsets.
    There will be some minor error in your plot unless you correct by math; hard to do in the wind or rain!
    Using the DM.M system is a little easier because all the distances will be in decimal parts of miles, which are easier to use quickly. Complicating the picture, though: latitude and longitude coordinates are not marked on the map in DM.M coordinates. You must use the distance scale to plot your fix.
Marking Your Position With UTM Using the UTM system, even with its queer number notation, is considerably easier. Several things are in our favor:
  • the grid blocks are squares;
  • the blocks are decimal multiples of 1000 meters square;
  • the first part of each position coordinate locates the lower left corner of our position square;
  • we read the last three digits of our position coordinates "right up" (east first, then north) to find our position;
  • the last three digits of our position coordinates are in direct meters on the ground.
Recall the coordinates for the junction of highways I25 and I40 in Albuquerque:
13S     351986E     38 85925N.

To mark your UTM position, first find the map grid square in which your fix is located:
  1. read from the zone central meridian to 351000E;
  2. read from the equator to 3885000N;

    then find your location in the square:

  3. read right 986 meters;
  4. read up 925 meters. You are there!
Locating a UTM fix
    Using the UTM system is so simple that transferring distances from the distance scale is not usually required— it can usually be done by eyeball estimation.

"How Accurate Will My Plot Be?"
    I mentioned in our last discussion of GPS fixes that ground precision should be judged only in terms of the performance you expect within a system's specifications. That's a fancy way of saying "fairly accurate."
    In almost every case a marked map fix will differ by a small amount from a real earth position. What's most important is where you are; second, where your map says you are.
    When you arrive at your marked point use landmarks and map to verify your position. Even then you'll probably have to search carefully to locate a particular landmark. When you find it take a compass fix and write it down; mark the landmark visually if you can.
    Don't worry too much about a degree or two of bearing error—five degrees is usually more than enough accuracy for orientation, which is, after all, using map and compass and terrain features.

It's Fun Time
    Up to now it's been words, words, words... and a few pictures. Orientation is a doing thing. Let's have some fun with a real map.
    Above I mentioned a 1/24,000 map that was imprinted with the UTM grid. Here's your assignment: contact the U. S. G. S. and order:
  1. a map catalog of your state
  2. U. S. G. S. map symbols brochure
  3. U. S. G. S. map "Los Indios Canyon, NM," #36106-F8-TF-024.
The first two items should be free; the third, about $4.00, all plus shipping. You should get your materials in about four weeks.
    Look in our Library for U. S. G. S. address, phone number, and Web map links.
    We'll use the Los Indios Canyon map as a reference for the rest of our navigation series. To get you going when you get your map:
What is located at 13S 326400 4046300?
What is the approximate elevation of that object?
What is the terrain like at that point?
Answers time after next.

    As an additional exercise, get a road map of your own home region and verify that it contains all the features mentioned above. You'll be surprised.

References
    While preparing this article I discovered that no one book had all the right information. I had to do a lot of editing and sorting. I've tried to express these basics clearly, as simply as I can. Here are some of the books I found useful:
  • Dutton's Navigation and Piloting, Benjamin Dutton, Elbert Maloney.
  • GPS Made Easy, Lawrence Letham.
  • Land Navigation Handbook, W. S. Kals (Sierra Club).
  • Mountaineering: The Freedom of the Hills, The Mountaineers.
  • U. S. Army FM 21-26, Map Reading and Land Navigation. The updated version of this field manual is actually available online: FM 3-25-26.
All of these titles but the army field manual are available from our Online Bookstore.
    For Internet tutorials on map and compass see the Navigation Education Links in our .
    See you next time for the next installment; subject: magnetic compasses.
-z-
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