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.
5l. 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. It 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 51).
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
100 meters is a regular football field plus 10 meters.
1,000 meters is 1 kilometer (km).
10 kilometers is 10,000) meters.
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 determined. There are two ways to do this:
(b) Determine 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 form:
MD = 4.32 centimeters
(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, determine the RF using the formula:
Ground Distance = 2,200 meters
RF = 1:50,000
MD = 2,200 meters ÷ 50,000
MD = 0.044 meter x 100 (centimeters per meter)
MD = 4.4 centimeters
52. 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 52). When using the graphic scale, be sure to use the correct scale for the unit of measure desired.
a. To determine straightline distance between two points on a map, lay a straightedged 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 53).
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 54).
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 determine 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 54). From the zero left to the end of the first shaded square is 100 meters. From the beginning of the center square to the left is 100 to 200 meters; at 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 winding 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 eightdigit 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 55A).
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 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 55B).
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).
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.
(4) When measuring distance in statute or nautical miles, round it off to the nearest onetenth 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.
|R = Rate of travel (speed )||T = Time|
(b) Find the length of the line to represent the distance at map scale--
(3) Divide the scale extension (left portion) into the desired number of lesser time divisions--
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 determine 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 determine 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 terrain. To determine your pace count on a 600meter 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.
(2) Certain conditions affect your pace count in the field, and you must allow for them by making adjustments.
(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.
(2) To convert miles to kilometers, devide the number of miles by 0.62.
(2) The following two procedures are involved in subtense measurement:
(3) The subtense base may be any desired length. However, if a 60meter base, a 2meter bar, or the length of an M16A1 or M16A2 rifle is used, precomputed subtense tables are available. The M16 or 2meter 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 2meter 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 2meter bar out to 250 meters, and with the 60meter base out to 1,000 meters. If a base of another length is desired, a distance can be computed by using the following formula:
(3) Proficiency, of methods. The methods discussed above are used only to estimate range (Table 51). 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.