In experiments made with a freight train on the Erie Railway in 1881, reported by Mr. F. M. Wilder to the Railway Master Mechanics’ Association, it was found that the total resistance on a level track was from 3.25 to 4.5 pounds per ton at speeds under twenty miles an hour. These figures will approximately represent the resistance due to wheel and axial friction in summer; but this resistance will be higher during cold weather, when the oil in the axle-boxes gets frozen. Track in bad condition will also tend to increase the wheel resistance, and improperly constructed trucks and wheels will entail the use of more power to move the train. Where trucks are so defective that they do not maintain the wheels revolving in parallel planes, the flanges of some of the wheels will rub on the rail, increasing the resistance. Wheels out of round; those having the axle out of center, however slight; wheels of different size on the same axle; and numerous other car-truck disorders,—all contribute their share in making a train pull hard.
CONDITIONS THAT INCREASE TRAIN RESISTANCES.
In a calm day the atmospheric resistance is very slight under a speed of twenty miles an hour. To a fast train, atmospheric resistance becomes an important obstruction. The atmosphere acts on the train in various ways, that are hard to calculate with any degree of accuracy,—head resistance to the locomotive, which is presumably equal to the exposed area of the front of the engine and cab in square feet multiplied by the air-pressure due to the speed; then, various parts of the cars present surfaces that the air strikes against, and increases the resistance; the raised and projecting roofs of passenger coaches offer an ample area for the wind to hold the train by; and every opening between the cars permits the wind to obstruct, to some extent, each individual car. Where wind is blowing freely in a direction to strike the train on the side, the resistance is greatly increased; the retardation being due to the wind pushing the car sidewise, so that the wheel-flanges rub against the rail, and also to the wind obtaining a strong hold on the front of each car. In the case of a freight train, the resistance is greatly increased when the doors of cars are left open; for every car in that condition acts like a parachute to reduce speed. Freight trains arranged with box cars and flat cars mixed, obtain more than a fair share of obstruction from the atmosphere; for every box car that has a space opened in front by a flat car, gets nearly the full pressure of the wind in its front. It pays in coal to incur some trouble and delay in putting box cars together. That also enables the brakemen to get along the train more rapidly than where the cars are mixed.
In the experiments already alluded to on the Erie Railway, it was found, in the absence of wind, that the first car of a freight-train produced atmospheric resistance equal to a surface of sixty-three feet, multiplied by the air-pressure due to speed; and that each subsequent car offered a resistance of twenty per cent of that due to the first car.
RESISTANCE OF CURVES.
Curved track increases the resistance of trains in direct proportion to the shortness of curvature. In European railways, the character of the curves is nearly always denominated by the length of radius: in this country, a railroad curve is described as of so many degrees. The degree of a curve is determined by the angle subtended at its center by a chord of 100 feet. To those who think of a curve by its radius, it may be well to explain that a curve of one degree has a radius of 5,370 feet, and the radius of any curve can be ascertained by dividing these figures by the number of degrees.
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.