Read an Excerpt
Wilderness Navigation Handbook
By Fred Touche, Anne Price
Touche PublishingCopyright © 2004 Fred Touche
All rights reserved.
Maps use patterns, colors, and symbols to describe a portion of Earth's surface. Maps are never exact, nor complete, representations of the real world. Different types of maps provide different kinds of information. For example, a road map may show cities, roads, and highways while ignoring terrain features such as valleys or mountain ranges. For off road navigation, topographic maps that use contour lines to describe the shape of the terrain are superior to other types of maps. For ocean and coastal navigation, nautical charts that show the shape of the underwater topography are the preferred choice.
When selecting a map, make sure that it includes the following: (1) legend, (2) scale, (3) contour interval, (4) grid lines, and (5) declination diagram. The legend tells you the meaning of the symbols, lines, and colors on the map. The scale and contour interval allow you to calculate distances, elevations, and slopes from the map. Grid lines make it easier to pinpoint a position on the map. The declination diagram shows you how to adjust your compass to compensate for Earth's irregular magnetic field.
The map legend shows the meaning of the colors and symbols on your map. Unfortunately, there is no worldwide standard so the colors and symbols may mean different things on different maps. This is why it is important to consult the legend before using a map from an unfamiliar series.
Since there are only a few colors to choose from, colors normally show entities that cover significant portions of the map. For example, vegetation zones are shown in green, bodies of water in blue, glaciers in white, urban areas in red, and areas with little or no vegetation in brown.
Map symbols are graphic representations of natural and man-made features. Point features such as campsites, lighthouses, or survey markers are shown as single symbols. Linear features such as roads, trails, power lines, railway tracks, rivers, or political boundaries are shown as dashed or continuous lines. Areas such as swamps, moraines, tidal flats, or sand dunes are shown as groups of identical symbols. Symbols are almost always shown at an exaggerated scale. Otherwise, they would be too small to be visible on the map.
All maps or charts are drawn to a specific scale. The scale is the relationship between a distance on the map versus the same distance in the real world. A large-scale map shows a small area in great detail, while a small-scale map covers a large area but with little detail. Selecting a map with an appropriate scale is therefore a compromise between coverage and detail, and depends on your intended activity. For example, climbing a mountain with complex topography requires a large-scale map, while a small-scale map may be a better choice for a long canoe trip. The scale that you see written on the map is just an approximation. It is never completely constant across the whole map, but varies according to the projection that was used to create the map. The larger the area that a map covers, the more susceptible it is to scale variations. The scale can be expressed as a verbal scale, a ratio scale, or a bar scale.
A verbal scale uses words to express the relationship between a distance on the map and the corresponding distance in the real world.
Example of verbal scale
The following is written in the margins of your map: "4 cm on the map represents 1 km on the ground." Here it is implied that a distance of 4 centimeters on the map is equal to 1 kilometer in the real world. This relationship allows you to calculate any other real world distance from the map. For example, a measured distance of 15.6 cm on the map represents (15.6 cm)/(4 cm) x 1 km = 3.9 km in the real world.
The scale of a map can be expressed as a ratio between a distance on the map versus the same distance in the real world. Some people find ratio scales confusing because distances are not tied to a specific unit. You can use any unit you want as long as you stick to the same unit during the conversion between map and real world distances. After doing the conversion, you can of course convert the resulting distance into other units.
Example of ratio scale
A map with "Scale 1:50 000" written in the margins means that the distance between any two points is 50 000 times longer in the real world than on the map. For example, a distance of 8.5 cm on the map would be 50 000 x 8.5 cm = 425 000 cm = 4250 m = 4.25 km in the real world.
A bar scale shows real world distances directly on the map. Bar scales are the most common type of scale, and are easy to understand because of their graphical nature. A common practice is to show several bar scales on the same map, each representing a different length unit. Bar scales are often shown together with ratio or verbal scales.
1.3 How to measure distances on a map
To calculate the real world distance of a proposed route, you must first measure the corresponding distance on the map. This is easy if the route is a straight line between two points. Simply measure the distance with a ruler. If you don't have a ruler, keep in mind that orienteering compasses often have rulers inscribed in their base plates. Another method is to use the grid lines that are drawn across some maps as a measuring device. The grid lines form an array of identical squares with sides of a specific length. After figuring out the dimensions of one square, the grid effectively becomes a ruler. For more complicated routes, break up your route into straight-line segments and measure the distance of each segment separately. Add the lengths of all the segments to calculate the total length of the route.
To measure a curved path, lay out a string along the route. Pinch the string with your fingers at the two end points of the route and then pull the string tight. Place the string along a ruler, or across grid squares, and read off the distance. If your map has a bar scale, place the string on the bar scale and directly read off the real world distance. Instead of a string, you can use a map wheel, also known as a curvimeter. Set the counter to zero and then roll the wheel along your route. The curvimeter will display the accumulated distance. Pay attention to the units. Curvimeters can either directly display real world distances for maps of certain scales, or just show the actual distance on the map. In the latter case, you must convert the map distance to the real world distance.
If you have access to digital maps and related software, a computer will calculate and display the distance of your route. A typical software package lets you create a route by clicking on your start point, end point, and any intermediate points. The program displays the cumulative distance between all the adjacent points. Some software packages allow you to trace curved routes on the digital map. This makes your calculated distance even more accurate.
1.4 Geographic coordinate system
The geographic coordinate system is one of the two widely used methods for pinpointing locations on a map. It covers Earth's entire surface. A location is identified by specifying its latitude (parallel) and longitude (meridian). Latitudes and longitudes can be visualized as an array of imaginary lines running along Earth's surface. A position is measured in angle units: degrees (°), minutes of arc ('), and seconds of arc ("). Each degree is subdivided into 60 minutes of arc, which in turn are subdivided into 60 seconds of arc. Sometimes decimal degrees are used instead of minutes and seconds of arc, or decimal minutes instead of seconds of arc. For example, 156°16'21" = 156°16.35' = 156.2725°.
The latitude of a location is defined as the angle between the equatorial plane and an imaginary line that drops vertically down from the location. This line generally does not intersect the equatorial plane exactly at Earth's center because Earth's surface is slightly flattened at the poles. The latitude is a measure of how far north or south a location is from the equator. Latitudes can be visualized as a series of concentric circles centered on the geographic poles and expanding to a maximum radius at the equator.
To specify the latitude, state the latitude angle and whether the position is north (N) or south (S) of the equator. The latitude is 90°N at the north pole, 0° at the equator, and 90°S at the south pole. Other locations have intermediate latitudes, for example, 46°25'09"S. The length along Earth's surface of one minute of latitude is proportional to the radius of curvature along the local surface; it varies from 1843 m at the equator to 1862 m at the poles. The original definition of the nautical mile was the average distance of one minute of arc of latitude along Earth's surface. Today, the nautical mile is defined as precisely 1852 m.
The longitude of a location is defined as the angle, parallel to the equatorial plane, between the location and a reference longitude called the prime meridian. By convention, the prime meridian (0°) is the longitude that runs through an established point at Greenwich, England. From there, other longitudes increase eastward and westward until they meet at 180° on the opposite side of Earth. The longitude is thus a measure of how far east (E) or west (W) a location is from the prime meridian.
Longitudes can be visualized as a series of north-south lines that converge at the poles. To specify the longitude, state the longitude angle and whether the position is east or west of the prime meridian, for example, 105°57'15"E. The length along Earth's surface of one minute of longitude varies from 1855 m at the equator to 0 at the geographic poles.
1.4.1 Geographic coordinates on maps
Major latitudes and longitudes are shown as lines across the map or as tick marks in the margins. On most maps or charts, only selected latitudes and longitudes are completely labeled. To prevent clutter, other lines are labeled with partial numbers. For example, only the minutes of arc are shown. The standard way to describe a location with geographic coordinates is to state the latitude followed by the longitude. For example, 46°25'09"S, 105°57'15"E.
For a rough approximation of the latitude and longitude of a location on a map, look at the nearest latitude and longitude lines that surround the location. Visually estimate where the location is relative to the nearest latitude and longitude lines. Take into account that there are 60 minutes of arc in each degree and 60 seconds of arc in each minute of arc.
For more precise results, use a ruler to measure the distance between the location and the nearest lower latitude line, and then measure the distance between the nearest higher and lower latitude lines. Divide the first distance by the second distance to obtain the proportional distance. Convert the proportional distance into angle units and then add the result to the nearest lower latitude line. Calculate the longitude in a similar manner.
Example of how to determine geographic coordinates on a map
On the map below, the proportional distance between Location A and the nearest lower latitude line is 17 mm/38 mm = 0.45. The angular distance between the latitude lines on the map is 1' = 60". Converting from proportional distance to angular units gives 0.45 x 60" = 27". Adding this result to the nearest lower latitude line gives 53°01'00"N + 27" = 53°01'27"N.
The proportional distance between Location A and the nearest lower longitude line is 32 mm/42 mm = 0.76. The angular distance between longitude lines is 2' = 2 x 60" = 120". Converting the proportional distance into angle units gives 0.76 x 120" = 91" = 1'31 ". Adding this result to the nearest lower longitude line gives 125°22'00"W + 1'31" = 125°23'31"W. The complete geographic position is written as 53°01'27"N, 125°23'31"W.
Similar types of calculations can be done to solve the reverse problem where you already have a written position and want to pinpoint it on the map. The above example clearly illustrates the trouble you have to go through to accurately determine a location with geographic coordinates. The task is even more difficult on maps where the latitude or longitude lines aren't straight.
1.5 Map projections
Projections are mathematical methods that are used to transfer geographic information from Earth's surface to maps. It is impossible to represent any portion of Earth's curved surface on a flat map without some kind of distortion of scale, direction, shape, or distance. The type of projection governs the type of distortion. Reducing one type of distortion will inevitably increase another type. Mapmakers are forced to compromise by deciding what sort of distortion is acceptable. This is largely determined by the intended use of the map.
Projections can be visualized as one or more light sources shining rays through Earth's surface onto a projection surface that may be partially located inside Earth. The rays produce an image of the topography and geographic coordinates on the projection surface. In areas where the projection surface is inside Earth, the image is formed by rays bouncing back from Earth's surface along the same path. The shape and location of the projection surface and the location(s) of the light source(s) define the type of projection. A map or chart is simply a portion of the projection surface.
The scale is always correct where the projection surface touches or cuts into Earth's surface. Features are shown too small where the projection surface is inside Earth and too large where the projection surface is outside Earth. Distances may be correct from one point to all other points, or from certain points to certain other points, but never from all points to all others points. In most cases, directions (bearings) do not follow straight lines. On large-scale maps, the distortion is usually minimal and can be safely ignored. Many types of projections exist, but only four widely used types are discussed here.
1.5.1 Mercator projection
In the Mercator projection, Earth's surface is projected onto a cylinder wrapped around the equator. A series of light sources are located along Earth's axis of rotation, with each source striking a particular portion of the projection surface.
The scale is correct only along the equator. Features are shown increasingly too large as you move away from the equator, becoming infinite at the poles. Shapes of small features are correct throughout the projection surface. Distances are correct only along the equator. Straight lines on the map have constant bearings but are generally not the shortest distance between two points.
The Mercator projection is not used for polar regions because of the extreme distortion of scale and shape of large features at high latitudes. It is a popular projection for ocean charts because a route that follows a constant bearing is always a straight line on the chart.
1.5.2 Lambert conformal conic projection
With the Lambert conformal conic projection, Earth's surface is projected onto a cone oriented with its apex over one of the geographic poles. The cone cuts through Earth along two latitudes called the standard parallels. The source is located along Earth's axis.
The scale is correct along the two standard parallels. Features between the standard parallels are shown too small, while features outside the standard parallels are shown increasingly too large. Shapes of small features are correct throughout the projection surface. Distances are correct only along the standard parallels. Bearings are correct only along the longitudes.
The Lambert conformal conic projection is well suited for maps with large east-west coverage and is used for some polar maps.
1.5.3 Universal transverse Mercator projection
The universal transverse Mercator (UTM) projection is complicated. The projection surface is a cylinder wrapped around Earth's poles along a longitude called the central meridian. The cylinder diameter is slightly smaller than Earth's diameter and cuts through Earth's surface along two lines parallel to the central meridian called secant lines. The light source is a series of points along Earth's axis of rotation. Only a narrow north-south strip, 3° of longitude on either side of the central meridian, is projected. For global coverage, the cylinder is twisted by 6° increments, creating an array of 60 different projection strips, each 6° of longitude wide.
Excerpted from Wilderness Navigation Handbook by Fred Touche, Anne Price. Copyright © 2004 Fred Touche. Excerpted by permission of Touche Publishing.
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