Whenever a road is laid out merely with the idea of passing through certain predetermined points and constructing the road as cheaply as possible, the usual result is that there will be a great variety of grades differing by small amounts from a level up to the actual maximum. In such cases it will usually happen that the term "ruling grade" will apply to only one or two grades along the entire length of the road. The length and weight of heavy trains will therefore be limited by these ruling grades, as already explained in the previous chapter. The obvious policy in such cases is to cut down these heaviest grades until some limit is reached, at which these heavy grades are so numerous and so long that any further reduction is financially, if not physically, impossible. The economics of such reduction of the ruling grade has already been considered in a previous chapter. It frequently happens that there are one or two grades along the line on which the tractive resistance is nearly, if not quite, twice the tractive resistance of any other grades on the line. In such cases the adoption of pusher grades becomes economical. If by using assistant engines to assist the heaviest trains over one or two steep grades, we are actually able to double the length or weight of our freight-trains, there is evidently an enormous saving, even though it requires the services of pusher-engines which are used for no other purpose.

203. Numerical Illustration Of The General Principle

In the following illustration the refinements regarding the hauling capacity of locomotives, as determined by rating tons, have been ignored. Assume that at one point on a road there is a grade of 1.9%, which is five miles long. Assume that all other grades are less than 0.92%. Assuming that all trains are to be operated by one engine throughout that division, the net capacity of a consolidation engine, weighing 107 tons, with 53 tons on the drivers, 9/40 adhesion, and six pounds per ton for normal resistance, will be 435 tons on the 1.9% grade. This is therefore the maximum net train-load allowable with that type of engine. Assume that this 1.9% grade has a length of five miles, and that the whole division is 100 miles long. By using pusher-engines on this five-mile grade the net train-load can be doubled. These 870 tons can also be hauled by one engine up the 0.92% grades. Making a rough comparison, which is free from details and allowances, we may say:

(a) Ten trains per day over a 100-mile division hauling. 435 tons net per train will require 1000 engine-miles per day, which will haul 4350 net tons.

(b) Utilizing pusher-engines on the steep grade, the same tonnage of 4350 tons may be handled in five trains of 870 tons each behind the locomotive. The engine mileage will be 5 x 100 miles of the through-engines plus 2 x 5 x 5 pusher-engine miles, which makes a total of 550 engine-miles per day, instead of 1000, to handle a given traffic.

The advantages of this method are numerous. (1) There is not only a large saving in the number of engine-miles, but it may even mean a saving in the number of locomotives, since it may require the purchase and use of ten locomotives in place of seven. (2) The throughengines, which are hauling 870 tons along the easier grades, are working more nearly to the limit of their capacity for a large part of the distance, and therefore are doing their work more economically. The work of overcoming the normal track resistances of so many loaded cars over so many miles of track, and of elevating so many tons of train weight through the differences of elevation of the several points of the line, is approximately the same whatever the exact route. If the grades are so made that fewer engines, which are working more constantly to nearly the limit of their capacity, can accomplish the work as well as more engines, which are doing but little work for a considerable proportion of the time, the economy is very apparent and unquestionable. Wellington expresses it very concisely: "It is a truth of the first importance that the objection to high gradients is not the work which the engines have to do on them, but it is the work which they do not do when they thunder over the track with a light train behind them, from end to end of a division, in order that the needed power may be attained at a few scattered points where alone it is needed".