The annexed figure is added, to explain the means of connecting the spiral c to the arms b of the propeller; the latter has a flange turning at right angles, through which a rivet is passed, as well as the spiral c, when they are both strongly united by riveting.
The advantage proposed to be derived from this invention, are, economy in the construction of railways, from the facility it affords for ascending inclined planes of almost any angle, and the consequent reduction of cuttings, embankments, bridges, etc.; also, inthe use of light rails instead of the heavy rails required for the locomotive system; and in the use of lighter carriages than those at present in use, and hence, less useless load.
Economy of power for locomotion, by the use of fixed engines, or water power in place of locomotive engines, and the consequent avoidance of the expense of erection and support of those costly establishments required for the latter.
Safety to passengers, by collision or the running of the trains off the rails being rendered impossible.
Before proceeding to give an estimate of the expense of construction, or of power for locomotion, on this system, it may be well to consider for a moment the amount of friction due to such a line of shafting as I propose, and also its power of resistance to tortion.
On the subject of friction, a good deal has been written, and many experiments are recorded, but I prefer taking my data from actual observation: I have therefore made several experiments on different lengths of shafting, some very favourable in their results, and others the reverse; the most unfavourable was one consisting of four different lengths at right angles to each other, and coupled by bevel-wheels; the result was something less than the 1/18th of the load, or 120 lbs. to the ton. I take this, being the least favourable, as the standard from which the following calculations are taken.
The weight of a mile and a half of the screw propeller, including gearing, will not exceed 80 tons, which at 120lbs. to the ton, leaves 9,6001bs. as the amount of friction; the bearings are 3 inches, and the pinion on the end of the shaft to which the power is applied 18 inches diameter, or as 6 to 1; therefore the power required to turn a line of shafting 80 tons weight, from a state of rest, applied at the periphery of the 18-inch pinion is l,600lbs., or 1/6th of 9,600lbs. The shafting is proposed to be formed of iron tubing, 4 inches diameter, and half an inch in thickness; the weight found by accurate calculation, and proved by experiment, as sufficient to twist such a shaft if applied to the periphery of an 18-inch pinion fast on it, is 22,196lbs.; now, as half the breaking weight may be applied, without producing any deflection, we have a shaft to which we may apply ll,100lbs. at the periphery of an 18-inch wheel, with perfect safety, without producing any tortion whatever. Now the power required to turn a mile and a half of screw propeller, from a state of rest, is l,6001bs., which is about 1/7 th of the power that may with perfect safety be applied to the 18-inch pinion, or, in other words, the shafting might be extended to seven times the length I have proposed without being subject to any tortion whatever.
With respect to the applicability of this system to curves, let us suppose the propeller to be laid down on a curve of 1,320 feet, or one quarter mile radius, and the shafting in lengths of 12 feet, it is evident that each length of shafting will form the base of an isosceles triangle, whose sides are 1,320 feet and base 12 feet, or as 110 to 1.
On calculating the angles at the base of this triangle, it will be found that the friction of the couplings, which are 3 inches diameter, will be something less than 1/36th of an inch, or 1/110th part of 3 inches.
Again, although the curve is formed of a series of straight pieces, 12 feet long each, yet as the versed sine of the arc of which the 12 feet length forms the chord is but a small fraction more than one quarter of an inch, it will be seen that so small a deviation from the curve cannot be so much as felt in practice.
With respect to the power required for this system, it has been shown that 1,600 lbs. applied to the periphery of an 18-inch pinion will be sufficient to overcome the inertia of a mile and a half of propeller, and set it in motion, round its axis. Now suppose the pitch of the screw to be 12 feet, then every revolution it makes on its axis impels the train 12 feet, and 154 revolutions per minute will impel the train at the rate of 21 miles an hour; to obtain this speed we require a spur wheel 5 1/2 times the diameter of the pinion, or 8 feet 3 inches in diameter, making 28 revolutions in a minute. If this spur wheel is turned by a 2 feet crank, the radius of wheel being 4 feet l 1/2 inch, it follows, that in order to apply a power equal to 1,600 lbs. at the periphery of the spur wheel, we must apply twice and one-sixteenth of that power, 3,300 lbs., to the crank; this power would be afforded by a condensing engine, 24-inch cylinder, 4 feel stroke, and making 28 strokes per minute, or 18 horse power.
The foregoing calculations are made without any reference to the provision spoken of, for bringing the propeller gradually into motion ; but as such provision is made, and it is known that half the power that is required to set a machine in motion is sufficient to continue that motion, we may safely calculate on one half the power above stated, or 800 lbs., as available for the purpose of propelling the trains. Now, as the circumference of the pinion is 4 feet 6 inches, and the pitch of the screw 12 feet, the effect will be as \\ to 12, and taking the friction of the train as 9 lbs. per ton, we have a power equal to the propulsion of 33 1/3 tons, or eight loaded carriages of more than 4 tons each ; but as one of the great advantages this system possesses over any other, is the facility it affords for transmitting a succession of trains at very short intervals, provision may thus be made for the most extensive traffic without increasing the engine power: for instance, a train capable of carrying 50 tons on the present system, could be divided into four trains of five or six. carriages each, at ten minutes intervals, an arrangement by which 900 tons of goods, or 12,900 passengers, might be conveyed in a day of twelve hours, and the expense of locomotion not exceeding six shillings per day, as may be seen by the following estimate, which includes interest on capital sunk in engines, engine-houses, and machinery, and the daily expense of locomotion.