The cars are first and third class, some open and some covered, and are constructed to hold twenty people, exclusive of the driver. At present, only one is fitted with a dynamo, but four more machines are now being constructed by Messrs. Siemens Bros., so that before the beginning of the heavy summer traffic five cars will be ready; and since two of these will be fitted with machines capable of drawing a second car, there will be an available rolling stock of seven cars. It is not intended at present to work electrically the portion of the line in the town at Portrush, though this will probably be done hereafter; and a portion, at least, of the mineral traffic will be left for the two steam-tramway engines which were obtained for the temporary working of the line pending the completion of the electrical arrangements.
Let us now put in a form suitable for calculation the principles with which Mr. Siemens has illustrated in a graphic form more convenient for the purposes of explanation, and then show how these principles have been applied in the present case.
Let L be the couple, measured in foot-pounds, which the dynamo must exert in order to drive the car, and w the necessary angular velocity. Taking the tare of the car as 50 cwt., including the weight of the machinery it carries, and a load of twenty people as 30 cwt., we have a gross weight of 4 tons. Assume that the maximum required is that the car should carry this load at a speed of seven miles an hour, on an incline of 1 in 40. The resistance due to gravity may be taken as 56 lb. per ton, and the frictional resistance and that due to other causes, say, 14 lb. per ton, giving a total resistance of 280 lb., at a radius of 14 inches. The angular velocity of the axle corresponding to a speed of seven miles an hour, is 84 revolutions per minute. Hence L = 327 foot pounds, and w = (2π × 84) / 60.
If the dynamo be wound directly on the axle, it must be designed to exert the couple, L, corresponding to the maximum load, when revolving at an angular velocity, w, the difference of potential between the terminals being the available E.M.F. of the conductor, and the current the maximum the armature will safely stand. This will be the case in the Charing-cross Electrical Railway. But when the dynamo is connected by intermediate gear to the driving wheels only, the product of L and w remains constant, and the two factors may be varied. In the present case L is diminished in the ratio of 7 to 1, and w consequently increased in the same ratio. Hence the dynamo, with its maximum load, must revolve at 588 revolutions per minute, and exert a couple of forty-seven foot-pounds. Let E be the potential of the conductor from which the current is drawn, measured in volts, C the current in amperes, and E the E.M.F. of the dynamo. Then E is proportional to the product of the angular velocity, and a certain function of the current.
For a velocity ω, let this function be denoted by f(C). If the characteristic of the dynamo can be drawn, then f(C) is known.
We have then
|E =||- - - -||f||(1.)|
If R be the resistance in circuit by Ohm's law,
|E - E|
|C =||- - - -|
|- - - - - - - -|
|Ω(E - CR)|
|w =||- - - -||(2.)|
Let a be the efficiency with which the motor transforms electrical into mechanical energy, then -
|Power required = L w =||a EC|
Dividing by w,
|L =||- - - - .||(3.)|
It must be noted that L is here measured in electrical measure, or, adopting the unit given by Dr. Siemens in the British Association Address, in joules. One joule equals approximately 0.74 foot pound. Equation 3 gives at once an analytical proof of the second principle stated above, that for a given motor the current depends upon the couple, and upon it alone. Equation 2 shows that with a given load the speed depends upon E, the electromotive force of the main, and R the resistance in circuit. It shows also the effect of putting into the circuit the resistance frames placed beneath the car. If R be increased, until CR is equal to E, then w vanishes, and the car remains at rest. If R be still further increased, Ohm's law applies, and the current diminishes. Hence suitable resistances are, first, a high resistance for diminishing the current, and consequently, the sparking at making and breaking of of the circuit; and, secondly, one or more low resistances for varying the speed of the car.
If the form of f(C) be known, as is the case with a Siemens machine, equations 2 and 3 can be completely solved for w and C, giving the current and speed in terms of L, E, and R. The expressions so obtained are not without interest, and agree with the results of experiment.
It may be observed that an arc light presents the converse case to a motor. The E.M.F. of the arc is approximately constant, whatever the intensity of the current passing between the carbons; and the current depends entirely on the resistance in circuit. Hence the instability of an arc produced by machines of low internal resistance, unless compensated by considerable resistance in the leads.
The following experiment shows in a striking form the principles just considered: An Edison lamp is placed in parallel circuit with a small dynamo machine, used as a motor. The Prony brake on the pulley of the dynamo is quite slack, allowing it to revolve freely. Now let the lamp and dynamo be coupled to the generator running at full speed. First, the lamp glows, in a moment it again becomes dark, then, as the dynamo gets up speed, glows again. If the brake be screwed up tight, the lamp once more becomes dark. The explanation is simple. Owing to the coefficient of self-induction of the dynamo machine being considerable, it takes a finite time for the current to obtain an appreciable intensity, but the lamp having no self-induction, the current at once passes through it, and causes it to glow. Secondly, the electrical inertia of the dynamo being overcome, it must draw a large current to produce the kinetic energy of rotation, i.e., to overcome its mechanical inertia; the lamp is therefore practically short-circuited, and ceases to glow. When once the rotation has been established, the current through the dynamo becomes very small, having no work to do except to overcome the friction of the bearings, hence the lamp again glows.
Finally, by screwing up the brake, the current through the dynamo is increased, and the lamp again short-circuited.
It has often been pointed out that reversal of the motor on the car would be a most effective brake. This is certainly true; but, at the same time, it is a brake that should not be used except in cases of emergency. For this reason, the dynamo revolving at a high speed, the momentum of the current is very considerable; hence, owing to the self-induction of the machine, a sudden reversal will tend to break down the insulation at any weak point of the machine. The action is analogous to the spark produced by a Ruhmkorff coil. This was illustrated at Portrush; when the car was running perhaps fifteen miles an hour, the current was suddenly reversed. The car came to a standstill in little more than its own length, but at the expense of breaking down the insulation of one of the wires of the magnet coils. The way out of the difficulty is evidently at the moment of reversal to insert a high resistance to diminish the momentum of the current.
In determining the proper dimensions of a conductor for railway purposes, Sir William Thomson's law should properly apply. But on a line where the gradients and traffic are very irregular, it is difficult to estimate the average current, and the desirability of having the rail mechanically strong, and of such low resistance that the potential shall not vary very materially throughout its length, becomes more important than the economic considerations involved in Sir William Thomson's law. At Portrush the resistance of a mile, including the return by earth and the ground rails, is actually about 0.23 ohm. If calculated from the section of the iron, it would be 0.15 ohm, the difference being accounted for by the resistance of the copper loops, and occasional imperfect contacts. The E.M.F. at which the conductor is maintained is about 225 volts, which is well within the limit of perfect safety assigned by Sir William Thomson and Dr. Siemens. At the same time the shock received by touching the iron is sufficient to be unpleasant, and hence is some protection against the conductor being tampered with.
Consider a car requiring a given constant current; evidently the maximum loss due to resistance will occur when the car is at the middle point of the line, and will then be one-fourth of the total resistance of the line, provided the two extremities are maintained by the generators at the same potential. Again, by integration, the mean resistance can be shown to be one-sixth of the resistance of the line. Applying these figures, and assuming four cars are running, requiring 4 horse power each, the loss due to resistance does not exceed 4 per cent. of the power developed on the cars; or if one car only be running, the loss is less than 1 per cent. But in actual practice at Portrush even these estimates are too high, as the generators are placed at the bottom of the hills, and the middle portion of the line is more or less level, hence the minimum current is required when the resistance is at its maximum value.
The insulation of the conductor has been a matter of considerable difficulty, chiefly on account of the moistness of the climate. An insulation has now, however, been obtained of from 500 to 1,000 ohms per mile, according to the state of the weather, by placing a cap of insulite between the wooden posts and T-iron. Hence the total leakage cannot exceed 2.5 amperes, representing a loss of three-fourths of a horse power, or under 5 per cent, when four cars are running. But apart from these figures, we have materials for an actual comparison of the cost of working the line by electricity and steam. The steam tramway engines, temporarily employed at Portrush, are made by Messrs. Wilkinson, of Wigan, and are generally considered as satisfactory as any of the various tramway engines. They have a pair of vertical cylinders, 8 inches diameter and one foot stroke, and work at a boiler pressure of 120 lb., the total weight of the engine being 7 tons. The electrical car with which the comparison is made has a dynamo weighing 13 cwt., and the tare of the car is 52 cwt.
The steam-engines are capable of drawing a total load of about 12 tons up the hill, excluding the weight of the engine; the dynamo over six tons, including its own weight; hence, weight for weight, the dynamo will draw five times as much as the steam-engine. Finally, compare the following estimates of cost. From actual experience, the steam-engine, taking an average over a week, costs -
|Coke, 58½ cwt. at 25s. per ton.||3||13||1½|
|Oil, 1 gallon at 3s. 1d.||0||3||1|
|Tallow, 4 lb. at 6d.||0||2||0|
|Waste, 8 lb. at 2d.||0||1||4|
|Depreciation, 15 per cent. on £750.||2||3||3|
|- - - - - -|
The distance run was 312 miles. Also, from actual experience, the electrical car, drawing a second behind it, and hence providing for the same number of passengers, consumed 18 lb. of coke per mile run. Hence, calculating the cost in the same way, for a distance run of 312 miles in a week -
|Wages of stoker of stationary engine.||1||0||0|
|Coke, 52 cwt. at 25s. per ton.||2||15||0|
|Oil, 1 gallon at 3s. 1d.||0||3||1|
|Waste, 4 lb. at 2d.||0||0||8|
|Depreciation on stationary engine, 10 per cent. on £300 11s. 6d.||}||2||0||4|
|Depreciation of electrical apparatus, 15 per cent. on £500, £1 8s. 10d.|
|- - - - - -|
A saving of over 25 per cent.
The total mileage run is very small, on account of the light traffic early in the year. Heavier traffic will tell very much in favor of the electric car, as the loss due to leakage will be a much smaller proportion of the total power developed.
It will be observed that the cost of the tramway engines is very much in excess of what is usual on other lines, but this is entirely accounted for by the high price of coke, and the exceedingly difficult nature of the line to work, on account of the curves and gradients. These causes send up the cost of electrical working in the same ratio, hence the comparison is valid as between the steam and electricity, but it would be unsafe to compare the cost of either with horse-traction or wire-rope traction on other lines. The same fuel was burnt in the stationary steam-engine and in the tramway engines, and the same rolling stock used in both cases; but, otherwise, the comparison was made under circumstances in favor of the tramway engine, as the stationary steam-engine is by no means economical, consuming at least 5 lb. of coke per horse-power hour, and the experiments were made, in the case of the electrical car, over a length of line three miles long, which included the worst hills and curves, and one-half of the conductor was not provided with the insulite caps, the leakage consequently being considerably larger than it will be eventually.
Finally, as regards the speed of the electrical car, it is capable of running on the level at the rate of 12 miles per hour, but as the line is technically a tramway, the Board of Trade Regulations do not allow the speed to exceed 10 miles an hour.
Taking these data as to cost, and remembering how this will be reduced when the water power is made available, and remembering such considerations as the freedom from smoke and steam, the diminished wear and tear of the permanent way, and the advantage of having each car independent, it may be said that there is a future for electrical railways.
We must not conclude without expressing our best thanks to Messrs. Siemens Bros. for having kindly placed all this apparatus at our disposal to-night, and allowing us to publish the results of experiments made at their works.
A paper recently read before the Society of Arts, London.