Part 19 (1/2)
_Comparison of Stationary and Locomotive Power._
In order clearly to set forth the reasons which justify the statement made by Mr. Brunel,[73] that stationary power if freed from the weight and friction of any medium of communication, such as a rope, must be cheaper than locomotive power, it is desirable to consider, (1) the waste of power which arises from the locomotive having to move itself as well as the train; and (2) the excess of cost at which a given power was supplied by a locomotive, as compared with that at which it could have been supplied by a stationary engine.
On the first point, the best information can be obtained from experiments made by Mr. Daniel Gooch during the gauge controversy. The results are very suitable for use in the present investigation, as the South Devon was to be a broad-gauge railway. Moreover, as the broad-gauge engine with which these experiments were tried was one of a cla.s.s more powerful for their weight not only than the contemporary narrow-gauge engine, but also than the engines Mr. Brunel had experience of when he wrote his report three years previously, the results may be considered to represent very favourably the then existing case for the locomotives.
The engine employed in the experiments weighed, with its tender, about fifty tons. The maximum power it was capable of delivering by the pressure of steam in its cylinders was represented as a tractive force of 4,900 lbs. at a speed of 60 miles an hour, equivalent to 784 indicated horse-power; and at 40 miles an hour 5,200 lbs., equivalent to 555 indicated horse-power.
It is next to be considered how this power would, when running at the speeds mentioned, be employed in overcoming the elements of resistance.
These are:--
(1) The working friction of the machinery.
(2) The rolling resistance of the engine and tender.
(3) The air resistance due to the engine frontage.
(4) The rolling resistance of the train.
(5) The air resistance on the portion of the train unprotected by the tender.
(6) The resistance due to gradient.
The following symbols and quant.i.ties may be conveniently made use of to denote the various terms of the equation between force and resistance.
Total available tractive force in lbs. F
Weight of engine and tender (superfluous load) in tons 50
Weight of train (useful load) in tons W
The sum of the resistances of machinery, rolling resistance, and air resistance of engine and tender R
Rolling resistance of train in lbs. per ton K
Gradient G
Speed in miles per hour V
Resistance of air (according to the received empirical formula)
1 = --- (frontage area) V^{2} 400
Frontage area of train in square feet 63
Frontage area of portion of train unprotected by the tender, in square feet 24
For a locomotive train therefore 24 F = R + WK + --- V^{2} + (50 + W) 2240 G.
400
For a system that dispenses with the locomotive
63 Tractive force = WK + --- V^{2} + W 2240 G.
400 Therefore
W (K + 2240 G) + 1575 V^{2}
= the useful tractive force, and
R + 112000 G - 0975 V^{2}
= the tractive force wasted by the use of the locomotive.
Therefore
F={R + 112000 G-0975 V^{2}} + {W (K + 2240 G) +1575 V^{2}}
and the useful load
(F- R - 112000 G - 06 V^{2}) W = ----------------------------- K + 2240 G.
The values which Mr. Gooch's experiments give for the two selected speeds are as follows[74]:--
+---------------+---------+-----------------+----------+
Miles per Hour
R (lbs.)
K (lbs. per ton)
F (lbs.)
+---------------+---------+-----------------+----------+
40
1500
125
5200
60
2100
186
4900
+---------------+---------+-----------------+----------+
Using these values, the results in the following table are obtained, being the conditions appropriate to the two speeds at successive ascending gradients:--
+------+---------+-------+-------+------+-------+------+------+-----------+
Miles
Ascending
Useful
Super-
Gross
Useful
Waste
Gross
Ratio of
per
Gradient
Load
fluous
Load
Horse-
Horse-
Horse-power
Hour
in tons
Load in
in tons
power
power
Waste to
tons
Useful
Horse-power
+------+---------+-------+-------+------+-------+------+------+-----------+
{
0
288
50
338
411
144
555
35
{
1/200
128
50
178
352
203
555
58
{