w
= a C ------- f(C)
[Omega]
Dividing by _w_,
a C f(C)
L = -------- . (3.)
[Omega]
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--
£ s. d.
Driver's wages. 1 10 0
Cleaner's " 0 12 0
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
----------
Total. £8 4 9½
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--
£ s. d.
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. }
Depreciation of electrical apparatus, 15 per cent. } 2 0 4
on £500, £1 8s. 10d. }
---------
Total. £5 19 1
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.
* * * * *