Popular Science Monthly/Volume 3/June 1873/Economy of Railway Locomotion
By J. W. GROVER, C.E.
THE primary conception of a railway is a perfectly smooth, level, and straight road, upon which friction is reduced to the minimum, so that heavy loads may be propelled with the least possible resistance, and at the highest rate of speed.
The earliest type of locomotive-engine was designed to run upon such straight and level roads, and it was supposed for many years that locomotives could not climb hills, or be made to go round corners.
The first railway-carriages were a simple modification of the stage-coaches, names and all. It is interesting to look at the curious three-bodied "Marquis of Stafford"—with yellow panels and windows, filled with ladies in large coal-scuttle bonnets—as shown in one of Ackermann's early engravings of the Liverpool and Manchester Railway, the only substantial difference being that, inasmuch as the railways of those days were made nearly straight, no arrangement was provided for allowing the axles of the carriage to radiate as they do partially in common road-vehicles, but both axles were rigidly fastened so as to be immovable.
Again, as all road-vehicles have to turn abrupt corners, their wheels are made to turn independently upon their axles, but, so soon as flanges were employed to keep the wheels of the railway-carriages between two straight rails, this arrangement was found unnecessary, and, to obtain greater strength and security, the wheels were rigidly fastened to the axle, and both were compelled to revolve together.
Now, since the primary conception of the perfectly smooth, straight road, a great degeneracy has been of necessity taking place; with greatly increased demands, less capital than ever has been forthcoming; consequently the great cuttings and embankments of early days are being abandoned as precedents, and it becomes necessary that railways should approach more closely to the form of ordinary roads, which follow the surface of the ground only, at small cost.
Hence it follows that the rolling-stock itself must revert more nearly to its original pattern, readopting those contrivances which, under altered circumstances, were discarded.
Let us keep to the most elementary principles, for it is these which are forgotten and misunderstood, and yet should be engraven on brass and hung up in every railway board-room in the world. On a common road, a horse can pull a ton weight in a cart behind him on the level at 4 to 4¼ miles an hour, or, which is the same thing, if a weight of 70 lbs. were hung over a pulley and lowered down a well, he could pull it up at the speed mentioned. It is necessary to be a little explicit, as the remarks in this paper are intended for non-technical readers particularly. Now, if two strips of iron called rails are laid upon the aforesaid road, the friction is reduced sevenfold; that is to say, the same horse at the same speed could draw 7 tons, the difference between macadam and iron being as 70 lbs. to 10 lbs. This immense advantage, however, disappears when gradients have to be encountered, because the resistance due to gravity becomes so greatly in excess of the resistance due to friction, and is constant in both cases. For instance, if on a common road, up a slope of one foot in ten, the horse takes 5 cwt. in a cart over the macadam, if rails be laid down up the same hill, he could only increase the burden behind him by a little more than 1 cwt., or, in all, 6¼ cwts.; hence, in this case, the value of the rails is nearly lost. Hence the small use of tramways where hills occur.
Upon a very good macadamized road the resistance due to friction is usually taken at about one-thirtieth of the whole load carried; that is to say, if the vehicle were put upon a road sloping 1 in 30, it would just begin to move of itself. But, upon a railway, under the most favorable conditions, the resistance due to friction has been reduced to the two-hundred-and-eightieth part of the whole load carried; that is to say, the vehicle will begin to move of itself on a gradient of 1 in 280. In considering the work which a horse can perform on a tramway, it is important to bear in mind the question of speed; for, according to the experiments of Tredgold, he can draw exactly four times as much at two miles an hour as he can at five, and it appears that, at three miles an hour, be does the greatest amount of actual useful work, whereas, at ten miles an hour, only one-fourth of his actual power is available, and he cannot exert that for an hour and a half; whereas, at two and a half miles an hour, he can continue working for eight hours. Having these data before us, it is easy to compare the values of steam and horse-flesh: Suppose coals to cost in the midland districts 18s. 8d. a ton only, or one-tenth of a penny per pound, and, assuming that an average locomotive-engine will not consume more than 5 lbs. of coal in the hour per horse-power, the cost of fuel per horse-power will be a halfpenny per hour. Taking the value of the horse's provender at 1s. 9d. a day only, and supposing he works for six hours, that would cost 3½d. an hour against a halfpenny in the case of steam, or, as 7 to 1 in favor of steam; and this result is obtained on the supposition that the horse travels only at three miles an hour.
Now, to sum up the combined advantages, therefore, of an engine on a level railway against a horse on a level common road at 10 miles an hour, we shall find that the former gives an economy over the latter of nearly 300 to 1; at 5 miles an hour, it would stand as 115 to 1; and, at 2½ miles an hour, as 64 to 1.
Such are the enormous advantages of steam and rails, and with them does it not seem astonishing that better financial results have not been obtained? There must be something wrong somewhere. As Artemus Ward says, "Why is this thus, and what is the reason of this thusness?"
Speed is the delinquent, and the cause of the loss of the great primary advantages: the vehicles on railways are propelled very fast; hence they involve great strength in their construction, and enormous weight in proportion to the paying load carried.
An old stage-coach, according to Nicholas Wood, weighed only 16 to 18 cwts., and would carry upward of 2 tons of paying passengers with their luggage, or about 4⁄10 of a hundred-weight of dead load to every hundred-weight of paying load. Now, a third-class carriage with four compartments would represent 2.8 cwts. of dead weight to every 1 cwt. of paying load. Therefore, the stage-coach has the advantage over the third-class railway-carriage of 6½ to 1.
It becomes impossible to institute any absolute comparison between roads and railways at speeds above 10 miles an hour, because such speeds are impossible on the former for any considerable distance. Again, the question of a gradient has to be noticed, for in the preceding remarks a level road and a level railway have only been considered.
As has been explained, where steep gradients occur, the resistance due to gravity so much outweighs that due to friction that rails afford a comparatively insignificant advantage, and one which is entirely lost if the stock has to be increased in weight 6½ times.
It may easily be shown that, on a gradient of 1 in 10, for instance, taking the foregoing figures, the advantages of a steam-worked railway over a horse-worked road would be little more than one-fourth, if the stock on the former be only 6½ times heavier in proportion than the latter would require. Hence it follows that no railway having gradients of 1 in 10 could be worth making (assuming such to be possible) unless the stock upon it were assimilated to that of the ordinary omnibus or stage-coach type.
In former times calculations were made by Nicholas Wood of the comparative costs of conveyance on ordinary roads by horses; he showed that on an average a stage-wagon could carry at the rate of 2½ miles an hour profitably at 8d. a ton per mile; that a light van or cart at 4 miles an hour could take for 1s. a mile a ton of goods. Passengers in stage-coaches were charged 3d. a mile each, or 3s. 6d. a ton, at 9 miles an hour. Now, let us consider what railways actually do. At the present moment coals are conveyed at ⅝d. per ton per mile, at an average speed of 20 miles an hour; and this low rate actually leaves a profit. Excursion-trains take passengers at less than ½d. each per mile, at twenty miles an hour, or at 7d. a ton a mile.
Now, bearing in mind the relative proportions of paying and non-paying loads involved in carrying passengers and coals, a simple calculation will show that a ton of passengers could be carried for something less than 1d. a mile, or 1⁄14 part of a penny each. For, although passengers require station accommodation, they unload themselves, which coals do not.
In the autumn of 1869, the Times took up the railway problem, and, in a series of very able articles, endeavored to show the errors of the present state of things. Although advocated by so powerful a pen, the reforms still remain unaccomplished—indeed, uncommenced. It was then shown that in practice every passenger on a railway involved over 2 tons—of iron and timber—to carry him. Or, according to Mr. Haughton, no more than 30 per cent, of the load which is hauled by a goods-train represents paying weight, the remaining 70 per cent, being dead weight. This seems astonishing truly, but it is nothing to the passenger-trains, where only 5 per cent., or even less, of the load pays, the remaining 95 per cent, being made up of apparently dead and unprofitable material. It is well to keep this clearly in view. In talking about a passenger, with relation to a railway, one must not picture to one's self a respectable English country gentleman, riding perhaps some 14 stone, but some Homeric giant, magnified into prehistoric proportions, weightier than an ordinary Ceylonese elephant, and representing about 20 to 25 full sacks of coal, or 21⁄4 tons.—Abstract from Quarterly Journal of Science.