The effects of grade on train expenses are of two distinct kinds. One possible effect is very costly and should be limited even at considerable expenditure. The other is of comparatively little importance, its cost being slight. As long as the length of a train is not limited by the power of the engine, the occurrence of a grade on a road merely means that the engine is required to develop so many foot-pounds of work in raising the train so many feet of vertical height. For example, if a train weighing 600 tons (1,200,000 pounds) climbs a hill 50 feet in height, the engine performs, in addition to the work due to mere tractive resistance and curvature, the extra work of creating 60,000,000 foot-pounds of potential energy. If this height is surmounted in two miles of horizontal distance (grade of 25 feet per mile) and in six minutes of actual time (20 miles per hour), the extra work accomplished by the engine is done at the rate of 10,000,000 foot-pounds per minute, which is about 303 horse-power. But the disadvantages of such a rise are always largely compensated. Except for the fact that one terminus of a road may be higher than the other, every up grade is followed more or less directly by a down grade, which is operated partly by the potential energy acquired during the previous climb. But when we consider the trains running in both directions, even the difference of elevation of the termini is largely neutralized. If we could eliminate altogether the waste of energy in the use of brakes, where brakes are used to control the train on grades, we would then find that the net effect of minor grades on their operation in both directions would be zero. Whatever was lost on any up grade would be regained on the succeeding down grade or on the return trip. On the very lowest grades, the limits of which are defined later, we may consider this to be literally true, viz., that nothing is lost by their presence. It is unnecessary to use brakes on these grades, except for such use as would be made if the line were level. Whatever energy is temporarily lost in climbing any grade is either immediately regained on a subsequent down grade or is regained on the return trip.
The other effect of grade is that it may so limit the length of trains that more trains will be required to handle a given traffic. The receipts from traffic are a perfectly definite sum which is independent of the number of trains. The cost of handling the traffic will be nearly proportional to the number of trains. Anticipating a more complete discussion, it may be said, as an example, that increasing the ruling grade from 1.20% (63.36 feet per mile) to 1.55% (81.84 feet per mile - an increase of about 18.5 feet per mile) will be sufficient to increase the required number of trains for a given gross traffic about 25%, i.e., five trains will be required to handle the traffic which four trains would have handled before at a cost slightly more than four-fifths as much. Since the gross receipts remain the same and the operating expenses have been increased nearly 20%, the effect on dividends is readily imagined. On the other hand, a reduction of the grade, which will enable four trains to handle an amount of traffic which have required five trains on the heavier grade, will have a corresponding influence in decreasing the operating expenses and will justify a large expenditure to accomplish this result.