Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

TOPOGRAPHICAL SKETCHING.

39. Topographical drawing includes every thing relating to an accurate representation upon paper, of any piece of ground. The state of cultivation, roads, town, county, and state boundaries, and all else that occurs in nature. The sketching necessary in railroad surveying, however, does not embrace all of this, but only the delineation of streams and the undulations of ground within that limit which affects the road, perhaps 500 feet on each side of the line. The making of such sketches consists in tracing the irregular lines formed by the intersection of the natural surface, by a system of horizontal planes, at a vertical distance of five, ten, fifteen, or twenty feet, according to the accuracy required.

Fig. 13.

40. Suppose that we wish to represent upon a horizontal surface a right cone. The base m m, fig. 13, is shown by the circle of which the diameter is m, m. If the elevation is cut by the horizontal planes a a, b b, c c, the intersection of these planes with the conical surface is shown by the circles a, b, c, in plan. The less we make the horizontal distances, on plan, between the circles, the less also will be the vertical distance between the planes.

Wishing to find the elevation of any line which exists on plan, as 1, 2, 3, 3, 2, 1, we have only to find the intersection of the verticals drawn through the points 1, 2, 3, 3, 2, 1, and the elevation lines a a, b b, c c; this gives us the curve 4, 5, 6, 7, 6, 5, 4.

Fig. 14.

41. Again, in fig. 14, the cone is oblique, which causes the circles on plan to become eccentric and elliptic. Having given the line 1, 2, 3, as before, we find it upon the elevation in the same manner.

42. In the section of regular and full lined figures, the horizontal and vertical projections are also regular and full lined; but in a broken surface like the ground, the lines become quite irregular.

Suppose we wish to show on plan the hill of which we have the plan, fig. 15, and the sections figs. 16, 17, and 18. Let AD be the profile (made with the level) of the line AD on plan, fig. 15. B E that of B E, and C F that of CF.

Fig. 15.

Fig. 16.

Fig. 17.

Fig. 18.

To form the plan from the profiles proceed as follows:—

Intersect each of the profiles by the horizontal planes a a, b b, c c, d d, equidistant vertically. In the profile A D, fig. 18, drop a vertical on to the base line from each of the intersections a, b, c, d, d, c, b, a. Make now A 1,1 2, 2 3, 3 4, etc., on the plan equal to the same on the profile. Next draw, on the plan, the line B E, at the right place and at the proper angle with A D; and having found the distances B 1, 1 2, 2 3, etc., as before, transfer them to the line B E on plan. Proceed in the same manner with the line C F.

The points a a a, b b b, c c c, are evidently at the same height above the base upon the profiles, whence the intersections of these lines with the surface line or 1 1 1, 2 2 2, 3 3 3, etc., on the plan, are also at the same height above the base; and an irregular line traced through the points 1 1 1, or 2 2 2, will show the intersection of a horizontal plane, with the natural surface.

When as at A we observe the contour lines near to each other, we conclude that the ground is steep. And when the distances are large, as at 6, 7, 8, we know that the ground falls gently. This is plainly seen both on plan and profile.

Fig. 15.

Having now the topographical sketch, fig. 15, we may easily deduce therefrom at any point a profile. If we would have a profile of G E, on plan, upon an indefinite line G E, fig. 19, we set off G 1, 1 2, 2 3, 3 4, etc., equal to the same distances on the plan. From these points draw verticals intersecting the horizontals a a, b b, c c; and lastly, through the intersections draw the broken line (surface line or profile) a, b, c, d, d, c, b, a. Thus we see how complete a knowledge of the ground a correct topographical sketch gives.

Fig. 19.

43. Field sketches for railroad work are generally made by the eye. The field book being ruled in squares representing one hundred feet each. When we need a more accurate sketch than this method gives, we may cross section the ground either by rods or with the level.

By making a very detailed map of a survey, and filling in with sketches of this kind, the location may be made upon paper and afterwards transferred to the ground.

So far we have dealt with but one summit; but the mode of proceeding is precisely the same when applied to a group or range of hills, or indeed to any piece of ground.

44. As a general thing, the intersection of the horizontal planes with the natural surface (contour lines) are concave to the lower land in depressions, and convex to the lower land on spurs and elevations. Thus at B B B b b, fig. 20, upon the spurs, we have the lines convex to the stream; and in the hollows c c c, the lines are concave to the bottom.

45. Having by reconnoissance found approximately the place for the road, we proceed to run a trial line by compass. In doing this we choose the apparent best place, stake out the centre line, make a profile of it, and sketch in the topography right and left.

Fig. 20.

Fig. 21.

Fig. 22.

Suppose that by doing so we have obtained the plan and profile shown in figs. 21 and 22, where A a a B is the profile of A C D B, on the plan. The lowest line of the valley though quite moderately inclined at first, from A to C, rises quite fast from C to the summit; and as the inclination becomes greater, the contour lines become nearer to each other.

Now that the line may ascend uniformly from A to the summit, the horizontal distances between the contour lines must be equal; this equality is effected by causing the surveyed line to cut the contours square at 1, 2, 3, 4, and obliquely at 5, 8, 10. Thus we obtain the profile A 5 5 B.

Figs. 23 and 24.

46. Having given the plan and profile, figs. 23 and 24, where A C D B represents the bed of the stream, in profile, if it were required to put the uniformly inclined line A m m B, upon the plan, we should proceed as follows. Take the horizontal distance A m from the profile, and with A (on plan) as a centre, describe the arc 1, 3. The point m on the profile is evidently three fourths of a division above the bed of the stream. So on the plan we must trace the arc 1, 3, until we come to a, which is three fourths of b c, from b. Again, m′ is nine and one half divisions above m. From a, with a radius m n on profile, describe the arc 4, 5, 6. Now, as on the profile, in going from m to m′, we cross nine contour lines, and come upon the tenth at m′, so on the plan we must cross nine contour lines and come upon the tenth, and at the same time upon the arc 4, 5, 6.

Proceeding in this way, we find A, a, b, B, on the plan, as corresponding to A m m′ B on the profile.

To establish in this manner any particular grade, we have first to place it upon the profile, and next to transfer it to the plan.

47. It may be remembered as a general thing, that the steepest line is that which cuts the contour line at right angles; the contour line itself is level, and as we vary between these limits we vary the incline.