Air Fronts: FM 21-26, Advanced Map and Aerial Photograph Reading - Section 4.

SECTION IV: MAP MEASUREMENTS

8. SCALE. Ground distance can be determined from a map by the map scale. Scale is the relation between distance on the map and actual distance on the ground. It is expressed in one or more of the following ways:

a. Words and figures. Scale may be expressed by a simple statement like "3 inches equals 1 mile," meaning 3 inches on the map equals 1 mile on the ground. Similarly, "l inch equals 200 feet" means that 1 inch on the map equals 200 feet on the ground.

b. Representative fraction. Scale may be shown by a fraction, called the representative fraction, abbreviated RF. The representative-fraction formula is:

Ground distance (GD) in which the numerator and denominator are expressed in the same unit, as inches, feet, yards, meters, or miles.

The RF appears in the margin as 1:20,000 or ,

which means 1 unit of distance on the map equals 20,000 such units on the ground. The larger the denominator of the RF, the smaller the scale of the map. Thus, a 1:1,000,000 map is a small-scale map and a 1:20,000 map is a large scale map. (See FM 21-25.)

c. Graphic scale. Distances may also be measured by the graphic scale-a special ruler for the particular map, printed in the margin. (See FM 21-25.)

9. MEASURING DEVICES.   a. Map measurer (fig. 1).

The map measurer is an instrument designed for quick measurement of distances or lines on a map. It consists of dial case, handle, and wheel or small roller. A moving pointer indicates on the dial the distance traveled by the wheel as it rolls along the line measured. To measure distance with a map measurer proceed as follows:

Figure 1. Map measurer.

(1) Turn the roller until the indicator is set at zero.

(2) Place the roller on one of the given points and, with the handle vertical, roll it along the line to the second point.

(3) The indicator will register the number of inches or centimeters traversed. To convert this map distance to ground distance, place the measurer roller on the zero of the scale and roll it backward along the scale until the indicator moves back to zero. Read ground distance.

b. Engineer scale. If the map's RF is known, distance between two points can be determined with a scale divided into inches. An engineer scale divided into tenths of an inch is best. To obtain the number of inches on the ground, measure the distance in inches between the two points on the map and multiply it by the denominator of the RF. Convert into feet by dividing by 12, into yards by dividing by 36, or into miles by dividing by 63,360. For example, figure 2 shows a portion of a map whose scale is 1:62,500. To find the distance on the ground between Missouri Mill and the road junction at Triangle proceed as follows: the engineer scale shows that the map distance between the points is 3.07 inches.

Figure 2. Measuring distance on a map with engineer's scale.

GD = MD x 62,500

GD = 3.07 x 62,500 = 191,875 inches to convert this distance into yards divide by 36:

10. CONVERSION FACTORS. Distances may be expressed in either the English or the metric system and it may be necessary to convert measurements of one system into those of another. Common units of metric linear measure and their English equivalents are:

1 mile = 1,760 yards = 1.609 kilometers =1,609 meters

1 kilometer = 1,000 meters = 1,094 yards = 0.62 mile.

1 meter 1.094 yards = 39.37 inches.

1 yard 0.91 meter = 36 inches.

11. DETERMINATION OF MAP SCALE. If the scale data are missing from the margin of a map, the RF of the map can be determined from a ground measurement or from a measurement on a map of known scale.

a. By measurement of distance between two points on the ground. The scale of a map may be determined by comparing the distance between two points on the ground with the distance between the same two points on the map. For example, in figure 3, the bridge and the crossroads are 3 inches apart on the map. The ground distance between the two points may be measured by tape, by striding, or by any other reasonably accurate method. Suppose the points are found to be 1,650 yards or 59,400 inches apart on the ground. Now substitute in the formula:

Figure 3. Scale of map may be determined when ground distance is known.

Map is apparently 1:20,000.

b. By measurement between two points on map of known scale. To determine the RF of a map with the aid of a map of known scale, select two points that appear on both maps and measure the distance between the two points. Then the ground distance between the two points can be figured from the map of known scale, and the scale of the other map may be determined by

Figure 4. Comparing scale of two maps representing identical area.

the process explained in a above. For example, in figure 4, map A has an RF of 1 -20,000 and the RF of map B is unknown. The distance between the crossroads and the house on map A is 10.2 inches; on map B it is 3.4 inches. The ground distance between the crossroads and house is determined from map A:

GD = MD x denominator of RF GD = 10.2 x 20,000 inches

Using this ground distance, the RF of map B is found by substituting in the formula:

rf of map B is 1:60,000.

12. TO CONSTRUCT A GRAPHIC SCALE. To construct a 5,000-yard graphic scale for use on a map whose RF is 1:20,000 proceed as follows:

a. Determine the length of the scale by the RF formula. In the formula the length of the scale is the map distance, 5,000 yards is the ground distance, and

is the RF. Ground distance of 5,000 yards must be converted to inches by multiplying by 36. Now substituting in the formula:

The scale must be 9 inches long to represent 5,000 yards.

b. Using an engineer scale, lay off the line ab 9 inches long (fig. 5).

c. Lay off, at any acute angle, line ab' representing 5 convenient equal divisions of the engineer scale.

Draw the line b'b, and through each division of the line ab' draw lines parallel to bb´. This divides line ab into 5 equal parts, each part representing 1,000 yards.

d. The 1,000-yard division at the left end of the scale is the extension and must be divided into 100-yard divisions. This is done by laying off the line ad', dividing it into 10 equal parts, and projecting these divisions to the extension as explained in c above.

e. Mark the divisions of the scale as shown in figure 5.

Figure5. Constructing graphic scale.

13. TIME AND DISTANCE. a. Conversion of distance to march time. To determine how long it will take to move troops from one point to another, first determine the distance between the two points by one of the methods explained in paragraphs 8 and 9. This distance divided by the hourly rate of march gives the time required to move the troops. The average daytime rate of march for foot troops, making allowance for customary halts, is 2½ mph.

b. Conversion of march tirne to distance. It is often necessary to determine the distance a column can march in a given time. The distance is the product of the time in hours and the hourly rate of march or D = T x R. For example, a motorized unit averaging 25 mph can cover 4 x 25 or 100 miles in 4 hours. This distance is measured along the road to locate the head of the column at the end of 4 hours. Thus the position of the head of the column at the end of any given time can be determined.

c. Rate of march. By substituting values of distance and time in the formula D = T x R and solving for R, the rate of march is determined.

14. TIME-DISTANCE SCALES. It may be desirable to construct a scale graduated into time intervals instead of distance intervals. This type of scale is useful in determining the position of a moving column at the end of any given time. For example, if an infantry column is marching 2½ mph, a time-distance scale in hours and minutes on a map whose RF is 1:62,500 is made as follows:

a. In 1 hour the column marches 2½ miles or 2½ x 63,360 inches or 158,400 inches.

b. To obtain the length of the scale to represent this distance on the map, substitute in the formula:

c. As shown in figure 6, lay off line ab on a sheet of paper. Then mark off on the scale as many 1-hour intervals of 2.53 inches as may be desired.

Figure6. Constructing time-distance scale.

The left interval. is the scale extension and may be divided into 1-minute, 5-minute, or 10-minute graduations, depending on the reading desired. The extension is divided by the method explained in paragraph 12c. Mark the graduations appropriately, indicate the RF of the map to which the scale applies, and indicate the marching rate of the column.