WORK DONE BY A LOCOMOTIVE PULLING A TRAIN.
To pull a train up an ascending gradient, the locomotive has to perform work similar to the operation of a pile-driving engine in raising its driving-block. The train is the block raised by the locomotive; and the lift is not vertical, but up an inclined plane; yet the amount of work done is reckoned in precisely the same way. When the engine of a pile-driver raises a block weighing 1,000 pounds a distance of 30 feet, the work done is 1,000 × 30 = 30,000 foot-pounds: when a locomotive pulls a train weighing 1,000 tons over one mile rising 30 feet, the engine performs 30,000 foot-tons of work in that distance by raising the load alone. The total amount of work done will also include the energy expended in overcoming wheel-friction and other ordinary train resistances.
To find the tractive force which the engine must exert through each foot of the mile traversed in pulling the train described, we must divide the foot-pounds of work done, by the distance over which the power was exerted. Thirty thousand foot-tons of work is 60,000,000 foot-pounds. To this we will add 5 pounds additional for every ton of the train for every foot advanced to cover wheel and wind resistances, making 86,400,000 foot-pounds of work that the engine has to perform in hauling the train one mile. This, divided by the number of feet in a mile, will give 16,363 pounds as the work the locomotive must perform through each foot,—an effort which is entirely within the capacity of many consolidation engines.