Manual of Military Training / Second, Revised Edition

CHAPTER I

1859. Definition of map. A map is a representation on paper of a certain portion of the earth's surface.

A military map is one that shows the things which are of military importance, such as roads, streams, bridges, houses, depressions, and hills.

1860. Map reading. By map reading is meant the ability to get a clear idea of the ground represented by the map,—of being able to visualize the ground so represented.

For some unknown reason, military map reading is generally considered a very difficult matter to master, and the beginner, starting out with this idea, seemingly tries to find it difficult.

However, as a matter of fact, map reading is not difficult, if one goes about learning it in the right way,—that is, by first becoming familiar with scales, contours, conventional signs, and other things that go to make up map making.

Practice is most important in acquiring ability in map reading. Practice looking at maps and then visualizing the actual country represented on the map.

1861. Scales. In order that you may be able to tell the distance between any two points on a map, the map must be drawn to scale,—that is, it must be so drawn that a certain distance on the map, say, one inch, represents a certain distance on the ground, say, one mile. On such a map, then, two inches would represent two miles on the ground; three inches, three miles, and so on. Therefore, we may say—

The scale of a map is the ratio between actual distances on the ground and those between the same points as represented on the map.

1862. Methods of representing scales. There are three ways in which the scale of a map may be represented:

1st. By words and figures, as 3 inches = 1 mile; 1 inch = 200 feet.

2d. By Representative Fraction (abbreviated R. F.), which is a fraction whose numerator represents units of distance on the map and whose denominator, units of distance on the ground.

For example, R. F. = 1 inch (on map)/1 mile (on ground) which is equivalent to R. F. = 1/63360, since 1 mile = 63,360 inches. So the expression, "R. F. 1/63360" on a map merely means that 1 inch on the map represents 63,360 inches (or 1 mile) on the ground. This fraction is usually written with a numerator 1, as above, no definite unit of inches or miles being specified in either the numerator or denominator. In this case the expression means that one unit of distance on the map equals as many of the same units on the ground as are in the denominator. Thus, 1/63360 means that 1 inch on the map = 63,360 inches on the ground, 1 foot on the map = 63,360 feet on the ground; 1 yard on the map = 63,360 yards on the ground, etc.

3d. By Graphical Scale, that is, a drawn scale. A graphical scale is a line drawn on the map, divided into equal parts, each part being marked not with its actual length, but with the distance which it represents on the ground. Thus:

For example, the distance from 0 to 50 represents fifty yards on the ground; the distance from 0 to 100, one hundred yards on the ground, etc.

If the above scale were applied to the road running from A to B in Fig. 2, it would show that the length of the road is 675 yards.

1863. Construction of Scales. The following are the most usual problems that arise in connection with the construction of scales:

1. Having given the R. F. on a map, to find how many miles on the ground are represented by one inch on the map. Let us suppose that the R. F. is 1/21120.

Solution

Now, as previously explained, 1/21120 simply means that one inch on the map represents 21,120 inches on the ground. There are 63,360 inches in one mile. 21,120 goes into 63,360 three times—that is to say, 21,120 is 1/3 of 63,360, and we, therefore, see from this that one inch on the map represents 1/3 of a mile on the ground, and consequently it would take three inches on the map to represent one whole mile on the ground. So, we have this general rule: To find out how many miles one inch on the map represents on the ground, divide the denominator of the R. F. by 63,360.

2. Being given the R. F. to construct a graphical scale to read yards. Let us assume that 1/21120 is the R. F. given—that is to say, one inch on the map represents 21,120 inches on the ground, but, as there are 36 inches in one yard, 21,120 inches = 21,120/36 yds. = 586.66 yds.—that is, one inch on the map represents 586.66 yds. on the ground. Now, suppose about a 6-inch scale is desired. Since one inch on the map = 586.66 yards on the ground, 6 inches (map) = 586.66 × 6 = 3,519.96 yards (ground). In order to get as nearly a 6-inch scale as possible to represent even hundreds of yards, let us assume 3,500 yards to be the total number to be represented by the scale. The question then resolves itself into this: How many inches on the map are necessary to represent 3,500 yards on the ground. Since, as we have seen, one inch (map) = 586.66 yards (ground), as many inches are necessary to show 3,500 yards as 586.66 is contained in 3,500; or 3500/586.66 = 5.96 inches.

Now lay off with a scale of equal parts the distance A-I (Figure 3) = 5.96 inches (about 5 and 91/2 tenths), and divided it into 7 equal parts by the construction shown in figure, as follows: Draw a line A-H, making any convenient angle with A-I, and lay off 7 equal convenient lengths (A-B, B-C, C-D, etc.), so as to bring H about opposite to I. Join H and I and draw the intermediate lines through B, C, etc., parallel to H-I. These lines divide A-I into 7 equal parts, each 500 yards long. The left part, called the Extension, is similarly divided into 5 equal parts, each representing 100 yards.

3. To construct a scale for a map with no scale. In this case, measure the distance between any two definite points on the ground represented, by pacing or otherwise, and scale off the corresponding map distance. Then see how the distance thus measured corresponds with the distance on the map between the two points. For example, let us suppose that the distance on the ground between two given points is one mile and that the distance between the corresponding points on the map is 3/4 inch. We would, therefore, see that 3/4 inch on the map = one mile on the ground. Hence 1/4 inch would represent 1/3 of a mile, and 4–4, or one inch, would represent 4 × 1/3 = 4/3 = 11/3 miles.

The R. F. is found as follows:

R. F. 1 inch/(11/3 mile) = 1 inch/(63,360 × 11/3 inches) = 1/84480.

From this a scale of yards is constructed as above (2).

4. To construct a graphical scale from a scale expressed in unfamiliar units. There remains one more problem, which occurs when there is a scale on the map in words and figures, but it is expressed in unfamiliar units, such as the meter (= 39.37 inches), strides of a man or horse, rate of travel of column, etc. If a noncommissioned officer should come into possession of such a map, it would be impossible for him to have a correct idea of the distances on the map. If the scale were in inches to miles or yards, he would estimate the distance between any two points on the map to be so many inches and at once know the corresponding distance on the ground in miles or yards. But suppose the scale found on the map to be one inch = 100 strides (ground), then estimates could not be intelligently made by one unfamiliar with the length of the stride used. However, suppose the stride was 60 inches long; we would then have this: Since 1 stride = 60 inches, 100 strides = 6,000 inches. But according to our supposition, 1 inch on the map = 100 strides on the ground; hence 1 inch on the map = 6,000 inches on the ground, and we have as our R. F., 1 inch (map)/6,000 inches (ground) = 1/6000. A graphical scale can now be constructed as in (2).

Problems in Scales

1864. The following problems should be solved to become familiar with the construction of scales:

Problem No. 1. The R. F. of a map is 1/1000. Required: 1. The distance in miles shown by one inch on the map; 2. To construct a graphical scale of yards; also one to read miles.

Problem No. 2. A map has a graphical scale on which 1.5 inches reads 500 strides. 1. What is the R. F. of the map? 2. How many miles are represented by 1 inch?

Problem No. 3. The Leavenworth map in back of this book has a graphical scale and a measured distance of 1.25 inches reads 1,100 yards. Required: 1. The R. F. of the map; 2. Number of miles shown by 1 inch on the map.

Problem No. 4. 1. Construct a scale to read yards for a map of R. F. = 1/21120. 2. How many inches represent 1 mile?

1865. Scaling distances from a map. There are four methods of scaling distances from maps:

1. Apply a piece of straight edged paper to the distance between any two points, A and B, for instance, and mark the distance on the paper. Now, apply the paper to the graphical scale, (Fig. 2, Par. 1862), and read the number of yards on the main scale and add the number indicated on the extension. For example: 600 + 75 = 675 yards.

2. By taking the distance off with a pair of dividers and applying the dividers thus set to the graphical scale, the distance is read.

3. By use of an instrument called a map measurer, Fig. 4, set the hand on the face to read zero, roll the small wheel over the distance; now roll the wheel in an opposite direction along the graphical scale, noting the number of yards passed over. Or, having rolled over the distance, note the number of inches on the dial and multiply this by the number of miles or other units per inch. A map measurer is valuable for use in solving map problems in patrolling, advance guard, outpost, etc.

4. Apply a scale of inches to the line to be measured, and multiply this distance by the number of miles per inch shown by the map.

1866. Contours. In order to show on a map a correct representation of ground, the depressions and elevations,—that is, the undulations,—must be represented. This is usually done by contours.

Conversationally speaking, a contour is the outline of a figure or body, or the line or lines representing such an outline.

In connection with maps, the word contour is used in these two senses:

1. It is a projection on a horizontal (level) plane (that is, a map) of the line in which a horizontal plane cuts the surface of the ground. In other words, it is a line on a map which shows the route one might follow on the ground and walk on the absolute level. If, for example, you went half way up the side of a hill and, starting there, walked entirely around the hill, neither going up any higher nor down any lower, and you drew a line of the route you had followed, this line would be a contour line and its projection on a horizontal plane (map) would be a contour.

By imagining the surface of the ground being cut by a number of horizontal planes that are the same distance apart, and then projecting (shooting) on a horizontal plane (map) the lines so cut, the elevations and depressions on the ground are represented on the map.

It is important to remember that the imaginary horizontal planes cutting the surface of the ground must be the same distance apart. The distance between the planes is called the contour interval.

2. The word contour is also used in referring to contour line,—that is to say, it is used in referring to the line itself in which a horizontal plane cuts the surface of the ground as well as in referring to the projection of such line on a horizontal plane.

An excellent idea of what is meant by contours and contour-lines can be gotten from Figs. 5 and 6. Let us suppose that formerly the island represented in Figure 5 was entirely under water and that by a sudden disturbance the water of the lake fell until the island stood twenty feet above the water, and that later several other sudden falls of the water, twenty feet each time, occurred, until now the island stands 100 feet out of the lake, and at each of the twenty feet elevations a distinct water line is left. These water lines are perfect contour-lines measured from the surface of the lake as a reference (or datum) plane. Figure 6 shows the contour-lines in Figure 5 projected, or shot down, on a horizontal (level) surface. It will be observed that on the gentle slopes, such as F-H (Fig. 5), the contours (20, 40) are far apart. But on the steep slopes, as R-O, the contours (20, 40, 60, 80, 100) are close together. Hence, it is seen that contours far apart on a map indicate gentle slopes, and contours close together, steep slopes. It is also seen that the shape of the contours gives an accurate idea of the form of the island. The contours in Fig. 6 give an exact representation not only of the general form of the island, the two peaks, O and B, the stream, M-N, the Saddle, M, the water shed from F to H, and steep bluff at K, but they also give the slopes of the ground at all points. From this we see that the slopes are directly proportional to the nearness of the contours—that is, the nearer the contours on a map are to one another, the steeper is the slope, and the farther the contours on a map are from one another, the gentler is the slope. A wide space between contours, therefore, represents level ground.

The contours on maps are always numbered, the number of each showing its height above some plane called a datum plane. Thus in Fig. 6 the contours are numbered from 0 to 100 using the surface of the lake as the datum plane.

The numbering shows at once the height of any point on a given contour and in addition shows the contour interval—in this case 20 feet.

Generally only every fifth contour is numbered.

The datum plane generally used in maps is mean sea level, hence the elevations indicated would be the heights above mean sea level.

The contours of a cone (Fig. 7) are circles of different sizes, one within another, and the same distance apart, because the slope of a cone is at all points the same.

The contours of a half sphere (Fig. 8), are a series of circles, far apart near the center (top), and near together at the outside (bottom), showing that the slope of a hemisphere varies at all points, being nearly flat on top and increasing in steepness toward the bottom.

The contours of a concave (hollowed out) cone (Fig. 9) are close together at the center (top) and far apart at the outside (bottom).

The following additional points about contours should be remembered:

(a) A Water Shed or Spur, along with rain water divides, flowing away from it on both sides, is indicated by the higher contours bulging out toward the lower ones (F-H, Fig. 6).

(b) A Water Course or Valley, along which rain falling on both sides of it joins in one stream, is indicated by the lower contours curving in toward the higher ones (M-N, Fig. 6).

(c) The contours of different heights which unite and become a single line, represent a vertical cliff (K, Fig. 6).

(d) Two contours which cross each other represent an overhanging cliff.

(e) A closed contour without another contour in it, represents either in elevation or a depression, depending on whether its reference number is greater or smaller than that of the outer contour. A hilltop is shown when the closed contour is higher than the contour next to it; a depression is shown when the closed contour is lower than the one next to it.

If the student will first examine the drainage system, as shown by the courses of the streams on the map, he can readily locate all the valleys, as the streams must flow through valleys. Knowing the valleys, the ridges or hills can easily be placed, even without reference to the numbers on the contours.

For example: On the Elementary Map, Woods Creek flows north and York Creek flows south. They rise very close to each other, and the ground between the points at which they rise must be higher ground, sloping north on one side and south on the other, as the streams flow north and south, respectively (see the ridge running west from Twin Hills).

The course of Sandy Creek indicates a long valley, extending almost the entire length of the map. Meadow Creek follows another valley, and Deep Run another. When these streams happen to join other streams, the valleys must open into each other.

1867. Map Distances (or horizontal equivalents). The horizontal distance between contours on a map (called map distance, or M. D.; or horizontal equivalents or H. E.) is inversely proportional to the slope of the ground represented—that it to say, the greater the slope of the ground, the less is the horizontal distance between the contours; the less the slope of the ground represented, the greater is the horizontal distance between the contours.

It is a fact that 688 inches horizontally on a 1 degree slope gives a vertical rise of one foot; 1376 inches, two feet, 2064 inches, three feet, etc., from which we see that on a slope of 1 degree, 688 inches multiplied by vertical rises of 1 foot, 2 feet, 3 feet, etc., gives us the corresponding horizontal distance in inches. For example, if the contour interval (Vertical Interval, V. I.) of a map is 10 feet, then 688 inches × 10 equals 6880 inches, gives the horizontal ground distance corresponding to a rise of 10 feet on a 1 degree slope. To reduce this horizontal ground distance to horizontal map distance, we would, for example, proceed as follows:

Let us assume the R. F. to be 1/15840—that is to say, 15,840 inches on the ground equals 1 inch on the map, consequently, 6880 inches on the ground equals 6880/15840, equals .44 inch on the map. And in the case of 2 degrees, 3 degrees, etc., we would have:

M. D. for 2° = 6880/15840 × 2 = .22 inch;

M. D. for 3° = 6880/15840 × 3 = .15 inch, etc.

From the above, we have this rule:

To construct a scale of M. D. for a map, multiply 688 by the contour interval (in feet) and the R. F. of the map, and divide the results by 1, 2, 3, 4, etc., and then lay off these distances as shown in Fig. 11, Par. 1867a.

FORMULA

M. D. (inches) = 688 × V. I. (feet) × R. F./Degrees (1, 2, 3, 4, etc.)

1867a. Scale of Map Distances (or, Scale of Slopes). On the Elementary Map, below the scale of miles and scale of yards, is a scale similar to the following one:

What is a slope of 1°? By a slope of 1° we mean that the surface of the ground makes an angle of 1° with the horizontal (a level surface. See Fig. 10, Par. 1867). The student should find out the slope of some hill or street and thus get a concrete idea of what the different degrees of slope mean. A road having a 5° slope is very steep.

By means of this scale of M. D.'s on the map, the map reader can determine the slope of any portion of the ground represented, that is, as steep as 1/2° or steeper. Ground having a slope of less than 1/2° is practically level.

1868. Slopes. Slopes are usually given in one of three ways: 1st, in degrees; 2d, in percentages; 3d, in gradients (grades).

1st. A one degree slope means that the angle between the horizontal and the given line is 1 degree (1°). See Fig. 10, Par. 1867.

2d. A slope is said to be 1, 2, 3, etc., per cent, when 100 units horizontally correspond to a rise of 1, 2, 3, etc., units vertically.

3d. A slope is said to be one on one (1/1), two on three, (2/3), etc., when one unit horizontal corresponds to 1 vertical; three horizontal correspond to two vertical, etc. The numerator usually refers to the vertical distance, and the denominator to the horizontal distance.

Degrees of slope are usually used in military matters; percentages are often used for roads, almost always of railroads; gradients are used of steep slopes, and usually of dimensions of trenches.

1869. Effect of Slope on Movements

• 60 degrees or 7/4 inaccessible for infantry;
• 45 degrees or 1/1 difficult for infantry;
• 30 degrees or 4/7 inaccessible for cavalry;
• 15 degrees or 1/4 inaccessible for artillery;
• 5 degrees or 1/12 accessible for wagons.

The normal system of scales prescribed for U. S. Army field sketches is as follows: For road sketches, 3 inches = 1 mile, vertical interval between contours (V. I.) = 20 ft.; for position sketches, 6 inches = 1 mile, V. I. = 10 ft.; for fortification sketches, 12 inches = 1 mile, V. I. = 5 ft. On this system any given length of M. D. corresponds to the same slope on each of the scales. For instance, .15 inch between contours represents a 5° slope on the 3-inch, 6-inch and 12-inch maps of the normal system. Figure 11, Par. 1867a, gives the normal scale of M. D.'s for slopes up to 8 degrees. A scale of M. D.'s is usually printed on the margin of maps, near the geographical scale.

1870. Meridians. If you look along the upper left hand border of the Elementary Map (back of Manual), you will see two arrows, as shown in Fig. 14, pointing towards the top of the map.

They are pointing in the direction that is north on the map. The arrow with a full barb points toward the north pole (the True North Pole) of the earth, and is called the True Meridian.

The arrow with but half a barb points toward what is known as the Magnetic Pole of the earth, and is called the Magnetic Meridian.

The Magnetic Pole is a point up in the arctic regions, near the geographical or True North Pole, which, on account of its magnetic qualities, attracts one end of all compass needles and causes them to point towards it, and as it is near the True North Pole, this serves to indicate the direction of north to a person using a compass.

Of course, the angle which the Magnetic needle makes with the True Meridian (called the Magnetic Declination) varies at different points on the earth. In some places it points east of the True Meridian and in others it points west of it.