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.

ALIGNMENT.

57. The broken line furnished by the survey is of course unfit for the centre line of a railroad. The angles require to be rounded off to render the passage from one straight portion to the other easy.

58. Let A X B, fig. 26, represent the angle formed by any two tangents which it is required to connect by a circular curve. It is plain that knowing the angle of deflection of the lines A X, B X, we obtain also the angles A C X, X C B. The manner of laying these curves upon the ground is by placing an angular instrument at any point of the curve, as at A, and laying off the partial angles E A a, E A M, E A G, etc., which combined with the corresponding distances A a, a M, M G, fix points in the curve.

These small chords are generally assumed at one hundred feet, except in curves of small radius (five hundred feet) when they are taken less.

The only calculation necessary in laying out curves, is, knowing the partial deflection to find the corresponding chord, or knowing the chord, to get the partial angle.

As the radius of that curve of which the angle of deflection is 1° is 5730 feet, the degree of curvature for any other radius is easily found. Thus the radius 2865 has a degree of curvature per one hundred feet of

again,

The radius corresponding to any angle is found by reversing the operation. If the angle is 3° 30′, or 210′, we have

The following figures show the angle of deflection for chords one hundred feet long, corresponding to different radii:—

Points in any curve may also be fixed by ordinates, as a b, M D′, G F, or by E a, K M, etc.

For the details of locating, of running simple and compound curves, and of the calculations therefor, the reader is referred to the works of Trautwine, and of Henck.

59. Suppose now that we have the surveyed lines m m, and n n, fig. 27, one of which is to be finally adjusted to the ground. The shortest line is the straight one, which is generally impracticable. The most level line is the contour line, which is also impracticable. Between these two lies the right line, which is to be found by an instrumental location. The line A n n n n B, on the plan, gives the profile A n n n n B. The line A m m m m B gives the profile A m m m m B, while the finally adjusted line A 1 2 3 4 5 6 gives the profile A 1 2 3 4 5 6 B.

60. Again, in fig. 28, the straight line A n n n B gives the profile A n n n B, requiring either steep grades or a great deal of work. By fitting the line to the ground, as by the line A a b c d ... m n o B, we obtain the profile A a b c ... m n o B.

61. The general arrangement of inclines must not be interfered with to save work, but a large part of the excavation and embankment may be saved by breaking up long grades so as not to affect materially the character of the road. Upon some lines the grades must necessarily undulate, as in fig. 29. The difference in the amount of work is plainly seen. The steepest grades thus applied must not be greater than the ruling grade upon the travel of one engine.

62. In long and shallow cuts and fills, the best plan is to place the grade line quite high, avoiding much cutting, and to make the embankments from side cuttings, (ditching). Banks must at least be placed two or three feet above the natural surface, first to prevent the snow from lodging too much upon the rails, second, to insure draining.

63. Snow fences are much used in the northern parts of the United States. These are high pieces of lattice-work, made roughly, but well braced; from eight to twelve feet high, and standing from sixty to one hundred feet from the road. The object of the fence is to break the current of the wind, and cause it to precipitate its snow. Close fences effect the object no better than the open ones, are more liable to blow down, and cost more.

64. In locating a road which is to have a double track eventually, regard must be paid to this fact in side-hill work. The first track should, if possible, be so placed as not to require moving when the double line is put on.

COMPARISON OF LOCATED LINES.

65. In this comparison there is an element which does not enter the approximate comparison of surveyed lines, curvature. The resistance arising from this cause has never been accurately determined. Mr. McCallum estimates the resistance at one half pound per degree of curvature per one hundred feet; i. e., the resistance due to curvature on a 4° curve, would be two lbs. per ton, (see report of September 30, 1855). Mr. Clark estimates the resistance due to curves of one mile radius and under, as 6.3 lbs. per ton, or twenty per cent. of the whole resistance. The average radius encountered, therefore, by Mr. Clark, would be, at Mr. McCallum’s estimate,

So small a radius is by no means allowable upon English roads; thus the estimate of Mr. Clark and of Mr. McCallum differ considerably. Experiments might easily be made with the dynamometer upon different curves, by which we might find very nearly the correct resistance caused by curves.

The curvature on any road cannot be adjusted to trains moving at different speeds.

66. The tractive power acts always tangent to the curve at the point where the engine is, and thus tends to pull the cars against the inner rail. The tangential force, generated by the motion of the cars, tends to keep the flanges of the wheels against the outer rail; and only when a just balance is made between the tractive and tangential forces, the wheel will run without impinging on either rail, (the wheel being properly coned). For these forces to balance, there must be a fixed ratio between the weight of a car and the speed, (not the weight of a train, as the shackling allows the cars to act nearly independently, some indeed rubbing hard for a moment against the rail, while the next car is working at ease). Whenever the right proportion is departed from, as it nearly always is, (and perhaps necessarily in some cases,) upon railroads, the wheels will rub against one rail or the other. Thus on any road where the speed on the same curve, or the radii of curvature under the same speed, differ, there must be loss of power, and dragging or pushing against the rails.

67. We are obliged to elevate the outer rail (see chapter XIII.), for the fastest trains, and the slower trains on such roads will therefore always drag against the inner rails. Thus in practice we generally find the inside of the outer rail most worn on passenger roads, and the inside of the inner rail upon chiefly freight roads.

68. It has been the practice of some engineers in equating for curvature, to add one fourth of a mile to the measured length for each 360° of curvature, disregarding the radius, as the length of circumference increases inversely as the degree of curvature.

69. Now in equating for grades, in doubling the power we do not double the expense of working. We however increase it more by curvature than we do by grades, because besides requiring double power, the wear and tear of cars and rails and all machinery is increased upon curves, which is not the case upon grades.

70. The analysis of expense (in Appendix F.) upon the New York system of roads, gives the following:—

Now each 360° will be equal to 75
100 of one quarter of a mile, or 75
400 of a mile; whence the number of degrees which shall cause an expense equal to one straight and level mile, will be 1920°.

71. The number of degrees by Mr. McCallum’s estimate would be thus:—

The resistance upon a level being ten lbs. per ton, and that due to curves one half pound per ton, per degree per one hundred feet; the length of a 2° curve to equal one mile will be

or ten miles. Also ten miles, or 530 hundred feet by 2° is 1060°.

72. Again, by Mr. Clark’s resistance of twenty per cent. of the level resistance, upon curves averaging 2°, we have as the length of 2° curve

or 265 hundred feet, which by 2° gives 530°.

73. Averaging the first and last, we have as the number of degrees which should be considered as causing an amount of expense equal to one straight and level mile, 1225°, which averaging with the estimated resistance by Mr. McCallum, gives finally 1142½° as causing an expense equal to one straight and level mile, or, in round numbers, 1140°.

74. Suppose now that we would know which of the lines below to choose.

Assuming the speed as twenty miles per hour, the number by which to equate for grades, see chapter II., is ninety-six, also the number of degrees for curvature 1140, whence,

and if the cost of construction is as the actual, and the cost of maintaining and working as the mean equated length, we have, as a final comparison,

or as

Here the extra grades on the one hand nearly equal the curvature and the extra length on the other hand.

75. As a further example in the comparison of competing lines, let us take the actual case of the location of the eastern part of the New York and Erie Railroad.

It was questioned which of the two lines between Binghampton and Deposit should be adopted, and also between the mouth of Callicoon Creek and Port Jervis.

Between A and c, fig. 30, were located the lines shown in the sketch, one following the Susquehanna river from A to B, thence crossing the dividing ridge between that river and the Delaware to Deposit (c). The other passing up the Chenango river to a, thence crossing first the summit M to the Susquehanna at L, and second the summit K, to Deposit (c). The elements of the two lines are as follows:—

Assuming the number by which to equate for grades, as 96, and the equating number of degrees of curvature as 1140°; equating for grades and curvature in both directions, we have,

Assuming the cost of working and of maintaining as $4,000 per mile, we have

giving the preference of $595,700 to the route A B c, notwithstanding that the estimate thereon exceeds that on B by $118,300. The route A B c was adopted.

Again, it was doubtful whether to adopt the route E F, in going from D to G, or the line I H. The following are the elements of the two lines:—

The mean equated lengths are as follows:—

The comparison as to cost is

and as to working,

and the sum as

Although the cost of E F is $401,480 more than that of I H, the line E F was adopted.