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

50. Between points at different elevations, we should if possible have no rise while descending, and consequently no fall while on the ascent.

51. Some engineers express themselves very much in favor of long levels and short but steep inclines. There are cases where the momentum acquired upon one grade, or upon a level, assists the train up the next incline. The distance on the rise during which momentum lasts, is not very great. A train in descending a plane does not receive a constant increase of available momentum, but arrives at a certain speed, where by increased resistance and by added effect of gravity, the motion becomes nearly regular. Up to this point the momentum acquired is useful, but not beyond.

Any road being divided into locomotive sections, the section given to any one engine should be such as to require a constant expenditure of power as nearly as possible; i. e., one section, or the run of one engine, should not embrace long levels and steep grades. If an engine can carry a load over a sixty feet grade, it will be too heavy to work the same load upon a level economically. It is best to group all of the necessarily steep grades in one place, and also the easy portions of the road; then by properly adapting the locomotives the cost of power may be reduced to a minimum.

As to long levels and short inclines the same power is required to overcome a given rise, but quite a difference may be made in the means used to surmount that ascent.

Fig. 25.

52. Suppose we have the profiles A E D and A B D, fig. 25. The resistance from A to D by the continuous twenty feet grade is the same as the whole resistance from A to B and from B to D. The reason for preferring A E D is, that an engine to take a given load from B to D would be unnecessarily heavy for the section A B; while the same power must be exerted at each point, of A E D. Also the return by A E D is made by a small and constant expenditure of power, being all of the way aided by gravity; while in descending by B, we have more aid from gravity than we require from D to B, after which we have none.

When the distances A B, B C, are sixty and twenty miles in place of six and two, we may consider the grades grouped at B D, and use a heavier engine at that point, as we should hardly find eighty miles admitting of a continuous and uniform grade.

EQUATING FOR GRADES.

53. In comparing the relative advantages of several lines having different systems of grades, it is customary to reduce them all to the level line involving an equal expenditure of power.