Manual of Military Training, James A. Moss [books under 200 pages .TXT] 📗
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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).
Fig. 7 Fig. 7 Fig. 8 Fig. 8 Fig. 9 Fig. 9The 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.
Slope (degrees) Rise (feet) Horizontal Distance (inches) 1 deg. 1 688 2 deg. 1 688/2 = 344 3 deg. 1 688/3 = 229 4 deg. 1 688/4 = 172 5 deg. 1 688/5 = 138
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.
FORMULAM. 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:
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