CHAPTER XXI.

=254. Introductory.=—The first step toward the construction of a railroad is the location of the line, which requires as an initiative a careful ocular examination of the general vicinity of the proposed road, supplemented by simple and approximate instrumental work rapidly performed. Following this reconnaissance, as it is called, more complete surveys and examinations are made both in the field and on the maps plotted from the data of the field-work. The prosecution of this series of operations produces the final location, together with the accumulation of such maps, profiles, and other data as may be required in the construction of the road-bed, bridges, and other structures constituting the complete railroad line with its ballast and track in place ready for traffic.

The ultimate purpose of any railroad line is the transportation of passengers and freight under conditions, including those of a physical nature connected with the road as well as the rates received, leading to profitable returns. Competition or other circumstances attending the traffic of a given road will fix the maximum rates to be charged for transportation. It is the business, first, of the civil engineer so to locate and design the road and, second, of the manager so to conduct the transportation as to make the margin of profits the greatest possible. It will be the purpose of this lecture to consider in a general way only some of the features of a railroad and its operation which are related directly to civil-engineering.

[Illustration: The Royal Gorge.]

=255. Train Resistances.=—It is a fact confirmed by constant daily experience that, however nicely the machine impelling the railroad train or the tracks supporting the cars may be built, considerable frictional and other resistance is offered to the movement of the train when the latter passes over a perfectly level and straight track.

A considerable portion of the cost of transportation is expended in overcoming this resistance. When the line fails to be either level or straight other resistances of magnitude are developed; they are called the resistances of grades and curves: and it is the business of the civil engineer so to design the railroad as to reduce these two classes of resistance to an absolute minimum, in view of certain other conditions which must be concurrently maintained.

=256. Grades.=—The grade of a railroad is expressed usually in this country by the number of feet through which 100 feet of length of line rises or falls, or by some expression equivalent to that. If, for instance, the line rises 1.5 or 2 feet in 100, it is said to have an ascending grade of 1.5 or 2 per cent. Or if the line falls the same amount in the same length, it is said to have a descending grade of 1.5 or 2 per cent. It is evident that a grade which descends in one direction would be an ascending grade for trains moving in the opposite direction, so that grades favoring traffic in one direction oppose it in the other. Hence, other things being equal, that road is the most advantageous for the movement of trains which has the least grade. The grades of railroads seldom exceed 2 or 2.5 per cent, although, as will presently be shown, there are some striking exceptions to that general observation. The actual angles of inclination of railroad tracks from a horizontal line are therefore as angles very small, but their disadvantages for traffic increase rapidly.

A simple principle in mechanics shows that if the railroad train with a weight _W_ moves up a 2 per cent grade, one component of the train weight acts directly against the tractive force of the locomotive or other motive power. If _a_ is the angle of inclination of the track to a horizontal line, this opposing component will have the value _W_ sin _a_. When angles are small their sines are essentially equal to their tangents. Hence, in this case, sin _a_ would have the value .02 or ¹/₅₀ of the train weight. If the weight of the train were 500 tons, which is a rather light train for the present time, this opposing force would be 10 tons, or 20,000 pounds, which, as we shall see later on, is more than one half of the total tractive force of any but the heaviest locomotives built at the present day. This simple instance shows the advantage of keeping railroad grades down to the lowest practicable values.

One of the most economical freight-carrying roads in the United States is the Lake Shore and Michigan Southern of the New York Central system, running from Buffalo to Chicago. Its maximum grade is 0.4 of 1 per cent. The maximum grade of the N. Y. C. & H. R. R. R. is 0.75 of 1 per cent between New York City and Albany and between Albany and Buffalo, 1.74 per cent at Albany, 1.12 per cent at Schenectady, and 1 per cent at Batavia. Pushers or assistant locomotives are used for heavy trains at the three latter points. The maximum grade of the Pennsylvania R. R. on the famous Horseshoe Curve between Altoona and Cresson is 1.8 per cent. It is advantageous, whereever practicable, to concentrate heavy grades within a short distance, as in the case of the New York Central at Albany, and use auxiliary engines, called pushers or assistants. Some of the heaviest grades used in this country are found on the trans-continental lines where they pass the summits of the Rocky Mountains or the Sierras. In one portion of its line over a stretch of 25.4 miles the Southern Pacific R. R. rises 2674 feet with a maximum grade of 2.2 per cent; also approaching the Tehacipi Pass in California the maximum grade is about 2.4 per cent. At the Marshall Pass on the Denver & Rio Grande R. R. there is a rise of 3675 feet in 25 miles with a maximum grade of 4 per cent. The Central Pacific R. R. (now a part of the Southern Pacific system) rises 992 feet in 13 miles with a maximum grade of 2 per cent. The Northern Pacific R. R. rises at one place 1668 feet in an air-line distance of 13 miles with a maximum grade of 2.2 per cent. Probably the heaviest grade in the world on an ordinary steam railroad is that of the Calumet Mine branch of the Denver & Rio Grande R. R., which makes an elevation of 2700 feet in 7 miles on an 8 per cent grade and with 25° curves as maximum curvature. These instances are sufficient to illustrate maximum railroad grades found in the United States.

=257. Curves.=—Civil engineers in different parts of the world have rather peculiar classifications of curves. In this country the railroad curve is indicated by the number of degrees in it which subtend a chord 100 feet in length. Evidently the smaller the radius or the sharper the curvature the greater will be the number of degrees between the radii drawn from the centre of a circle to the extremities of a 100-feet chord. American civil engineers use this system for the reason that the usual tape or chain used in railroad surveying is 100 feet long. A very simple and elementary trigonometric analysis shows that under this system the radius of any curve will be equal to 50 divided by the sine of one half of the angle between the two radii drawn to the extremities of the 100-feet chord. In other words, it is equal to 50 divided by the sine of one half the degree of curvature. The application of this simple formula will give the following tabular values of the radii for the curves indicated:

Curve. Radius in Feet.

1° 5729.65 2° 2864.93 3° 1910.08 4° 1432.69 5° 1146.28 6° 955.36 7° 819.02 8° 716.78 9° 637.27 10° 573.69 12° 478.74 15° 383.06 20° 287.91

=258. Resistance of Curves and Compensation in Grades.=—Inasmuch as the resistance offered to hauling the train around a curve increases quite rapidly as the radius of curvature decreases, it is obvious that in constructing a railroad the degree of each curve should be kept as low as practicable, and that there should be no more curves than necessary. While no definite rule can be given as to such matters, curves as sharp as 10° (573.69 feet radius) should be avoided wherever practicable. It is not advisable to run trains at the highest attainable speeds around such curves, nor is it done. Inasmuch as curve resistance has considerable magnitude, as well as the resistance of grades, it is natural that wherever curves occur grades should be less than would be permissible on straight lines or, as they are called, tangents. If a maximum gradient is prescribed in the construction of a railroad, that gradient will determine the maximum weight of train which can be hauled on the straight portions or tangents of the road. If one of these grades should occur on a curve, a less weight of train could be handled by the same engine than on a tangent. Hence it is customary to reduce grades by a small amount for each degree of curvature of a curve. This operation of modifying the grades on curves so as to enable a locomotive to haul the same train around them as up the maximum grade on a tangent is called compensating the curves for grade. There is no regular rule prescribed for this purpose, because the combination may necessarily vary between rather wide limits in view of speed, condition of track, and other influencing elements. The compensation, however, has perhaps frequently been taken as lying between .03 and .05 per cent of grade for each degree of curvature. In other words, for a 5° curve the grade would be .15 to .25 per cent less than on a tangent. This compensation for grades is carefully considered in each case by civil engineers in view of experience and such data as special investigations and general railroad operation have shown to be expedient.

[Illustration: FIG. 1. GRAVEL BALLAST]

[Illustration: FIG. 2. STONE BALLAST

NEW YORK CENTRAL & HUDSON RIVER RY.]

[Illustration: FIG. 3. PENNSYLVANIA RY.]

=259. Transition Curves.=—High speeds for which modern railroads are constructed have made it necessary not only to protect road-beds, but also to make the passage from tangents to curves as easy and smooth as possible. This is accomplished by introducing between the curve and the tangent at each end what is called a “transition” curve. This is a compound curve, i.e., a curve with varying radius. At the point where the tangent or straight line ceases the radius of the transition curve is infinitely great, and it is gradually reduced to the radius of the actual curve at the point where it meets the latter. By means of such gradual change of curvature the trucks of a rapidly moving train do not suddenly pass from the tangent to the curve proper, but they pass gradually from motion in a straight line to the sharpest curvature over the transition curve. The rate of transition is fixed by the character of the curves, which have been subjected to careful analysis by civil engineers, and they can be found fully discussed in standard works on railroad location.

[Illustration: FIG. 4.—Baltimore Belt-line Tunnel, B. & O. Ry.]

=260. Road-bed, including Ties.=—Not only the high rates of speed of modern railroad trains but the great weights of locomotives and cars have demanded a remarkable degree of perfection in the construction of the road-bed and in the manufacture of rails. The favorite ballast at the present time for the best types of road-beds is generally broken stone, although gravel is used. The first requisites are a solid foundation and perfect drainage whether in cuts or fills. Figs. 1, 2, 3, and 4 show two or three types of road-bed used by the New York Central and Hudson River R. R., the Pennsylvania R. R., and a special type adopted by the B. & O. for the belt-line tunnel at Baltimore. These sections show all main dimensions and the provision made for drainage. The general depth of ballast is about 18 inches, including the drainage layer at the bottom. The total width of road-bed for a double-track line varies frequently between 24 and 25 feet, while the width of a single-track line may be found between 13 and 14 feet. In the cross-sections shown the requirements for drainage are found to be admirably met. Timber ties are almost invariably used at the present time in this country, although some experimental steel ties have been laid at various points. Fig. 5 shows the steel tie adopted for experiment on the N. Y. C. & H. R. R. R. within the city limits of New York. The time will undoubtedly come when some substitute for timber must be found, but the additional cost of steel ties at the present time does not indicate their early adoption.

[Illustration: FIG. 5.]

[Illustration: FIG. 6.]

[Illustration: Cañon of the Rio Las Animas, near Rockwood.]

=261. Mountain Locations of Railroad Lines.=—The skill of the civil engineer is sometimes severely taxed in making mountain locations of railroads. Probably no more skilful engineering work of this kind has ever been done than in the crossings of the Rocky Mountains and the Sierras in this country by trans-continental railroad lines, although more striking examples of railroad location for short distances may perhaps be found in Europe or other countries. The main problem in such

cases is the making of distance in order to attain a desired elevation without exceeding maximum grades, such as those which have already been given. Most interesting engineering expedients must sometimes be resorted to. One of the oldest of these is the switchback plan shown in Fig. 6. This is probably the simplest procedure in order to make distance in attaining elevation. The line is run up the side of a mountain at its maximum grade as far in one direction as it may be desirable to go. It then runs back on itself a short distance before being diverted so as to pass up another grade in the reverse direction. This zigzagging of alignment may obviously be made to attain any desired elevation and so overcome the summit of a mountain range. The old switchback coal road near Mauch Chunk, Pa., is one of the oldest and more famous instances of the method, which has many times been employed in other locations.

[Illustration: FIG. 7.]

A more striking method, perhaps, is that of loops by which the direction of a line or motion of a train on it is continuous. Distance is made by a judicious use of the topography of the locality so as to run the line as far up the side of the valley as practicable and then turn as much as a semicircle or more, sometimes over a bridge structure and sometimes in tunnel, so as to give further elevation by running either on the opposite side of the valley or on the same. A succession of loops or other curves suitably located will give the distance desired in order to reach the summit.

=262. The Georgetown Loop.=—Fig. 7 shows one of these spiral or loop locations on the Georgetown branch of the Union Pacific Railroad in Colorado. It is a well-known and prominent instance of railroad location of this kind. On the higher portion of this loop system included in the figure there is a viaduct on a curve which crosses the line 75 feet above the rail below it and 90 feet above the water. This location is a specimen of excellent railroad engineering. The length of line shown in the figure, including the spiral, is 8½ miles, and it cost $265,000 per mile exclusive of the bridges.

=263. Tunnel-loop Location, Rhætian Railways, Switzerland.=—In Figs. 8 and 9 are shown two portions of the Albula branch of the Rhætian Railways, Canton Graubünden, southeastern Switzerland. The line connects the valleys of the Albula and the Inn, the former being one of the branches of the Rhine and the latter of the Danube; it therefore cuts the divide between the watersheds of those two rivers. It is a 3.28-feet gauge single-track road, and is built largely for tourist traffic, as the scenic properties of the line are remarkable.

The maximum grade on this line is 3.5 per cent. Over one portion of the line 7.8 miles long one third of that distance is in tunnel and 15 per cent of it on viaducts. The radii of the centre lines of the tunnels are 460 and 394 feet, while the lengths of the tunnels range from 1591 to 2250 feet, with a maximum grade in them of 3 per cent. The weight of rails used is 50 pounds per yard on grades of 2.5 per cent or less, but for heavier grades 55-pound rails are employed. The cross-ties are of mild steel and weigh 80 pounds each except in the long Albula tunnel, where treated oak ties are used as being better adapted to the special conditions existing there. It will be observed that in each case the line rises from the left-hand portion of the figure toward the right.

[Illustration: FIG. 8.]

[Illustration: FIG. 9.]

The tunnels are represented by broken lines, and they are in every instance on circular curves. Fig. 9 represents the line running from a point on the east side of the Albula River through a heavy cut and then across the valley of the Albula into a tunnel 2250 feet long. The line then runs chiefly in cuts to a point where there are two tunnels, one over the other; indeed the line over-laps itself in loops and tunnels a number of times in that vicinity. That portion of the road shown in Fig. 8 is less remarkable than the other, although it exhibits extraordinary alignment. This example of railroad location is one of the most striking among those yet completed. It would appear to indicate that no topographical difficulties are too great to be overcome by the civil engineer in railroad location in a most rugged and precipitous country. Obviously such a line could not be economically operated for heavy freight traffic.

Railroad lines frequently lead through mountainous regions affording some of the grandest scenery in the world accessible to the travelling public. In this country the Canadian Pacific, the Northern Pacific, the Great Northern, and the Rio Grande Western probably exhibit the most remarkable instances of this kind.