Note: Comparison of Stationary and Locomotive Power.
In order clearly to set forth the reasons which justify the statement made by Mr. Brunel, [1] 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 class 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 quantities 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) | ||||
| = | 1 400 |
(frontage area) × V2 | ||
| 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
| F = R + WK + | 24 400 |
V2 + (50 + W) 2240 G. |
For a system that dispenses with the locomotive
| Tractive force = WK + | 63 400 |
V2 + W 2240 G. |
Therefore
| W (K + 2240 G) + ·1575 V2 |
| = the useful tractive force, and |
| R + 112000 G – ·0975 V2 |
| = the tractive force wasted by the use of the locomotive. |
Therefore
F={R + 112000 G-·0975 V2} + {W (K + 2240 G) +·1575 V2}
and the useful load
| W | (F- R – 112000 G – ·06 V2) |
| K + 2240 G. |
The values which Mr. Gooch’s experiments give for the two selected speeds are as follows [2]:—
| Miles per Hour | R (lbs.) | K (lbs. per ton) | F (lbs.) |
| 40 | 1500 | 12·5 | 5200 |
| 60 | 2100 | 18·6 | 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 per Hour |
Ascending Gradient |
Useful Load in tons |
Super- fluous Load in tons |
Gross Load in tons |
Useful Horse-power |
Waste Horse-power |
Gross Horse-power |
Ratio of Waste to Useful Horse-power |
| 40-{ | 0 | 288 | 50 | 338 | 411 | 144 | 555 | ·35 |
| 1/200 | 128 | 50 | 178 | 352 | 203 | 555 | ·58 | |
| 1/100 | 71 | 50 | 121 | 292 | 263 | 555 | ·90 | |
| 1/75 | 50 | 50 | 100 | 252 | 303 | 555 | 1·20 | |
| 1/50 | 23·8 | 50 | 73·8 | 173 | 382 | 555 | 2·21 | |
| 1/40 | 11·7 | 50 | 61·7 | 113 | 442 | 555 | 3·91 | |
| 1/36·3 | 7 | 50 | 57 | 82 | 473 | 555 | 5·77 | |
| 60-{ | 0 | 139 | 50 | 189 | 504 | 280 | 784 | ·56 |
| 1/200 | 68 | 50 | 118 | 415 | 369 | 784 | ·89 | |
| 1/100 | 35·7 | 50 | 85·7 | 325 | 459 | 784 | 1·41 | |
| 1/75 | 22·5 | 50 | 72·5 | 265 | 519 | 784 | 1·96 | |
| 1/52·3 | 7 | 50 | 57 | 160 | 624 | 784 | 3·90 |
Thus, on a level line, the engine, working up to 555 horse-power, could just draw 288 tons of train at the rate of 40 miles per hour, wasting on its own resistance only one-third of the power usefully employed on the train; but when the speed was increased to 60 miles per hour, it could not, though working up to 784 horse-power, draw more than 139 tons of train, wasting on its own resistance more than half the power usefully employed on the train. And again, at 40 miles per hour, though, as just stated, it could draw on the level 288 tons, it could only draw 24 tons of useful load at that speed up 1 in 50; while at 60 miles per hour, though it could draw, as stated, 139 tons of train on the level, it could only draw 23 tons of useful load up 1 in 75; and at the respective speeds of 40 and 60 miles per hour, it could only take one carriage (7 tons) up the respective gradients of 1 in 36, and 1 in 52.
Hence to maintain a minimum speed of 40 miles per hour with locomotive power on a line with long gradients of 1 in 40 involved on those parts of the line a wasted power of nearly 4 times that usefully employed; and if a minimum limit of 60 miles per hour were contemplated, a locomotive of the most powerful class in existence three years subsequent to Mr. Brunel’s report advising the adoption of the Atmospheric System would only have been able to take a single carriage up an incline of 1 in 52. So heavily at high speeds on steep gradients is the performance of a locomotive taxed by the resistance due to its own dead weight. [3]
A comparison has now to be made between the cost of power as developed by a locomotive and as developed by a stationary engine.
From the well-known experiments made for the information of the Gauge Commissioners in December 1845, taking the high speed trials as the basis of calculation, it appears that 4·5 lbs. of coke per horse-power per hour may be taken as the average consumption of the engine. [4]
It will be well, however, to allow for the improvement which was at the time anticipated in locomotive working, and to assume an expenditure of 4 lbs. of coke per indicated horse-power per hour, as representing the case then for the locomotive engine.
Coke may be taken to have at that time cost 21s. a ton, or ·0094s. per lb. Moreover, a careful analysis of the Great Western Railway half-yearly reports, for 1844 and 1845, shows that for every shilling expended in coke, 1·44 shillings were expended on the average in wages, oil and waste, repairs, etc.
Putting the results together, it appears that for each single indicated horse-power delivered by a high-speed locomotive, the cost per hour was 0·0915s. or 1·098d.; that is to say, about 11/10 d.per hour.
Let this now be compared with the cost per horse-power per hour at which the best Cornish pumping engines had long been known to perform the work. This comparison is manifestly a rational one—with reference to the kindred employment of engine power in atmospheric pumping-engines.
The performances of nearly all the pumping-engines in Cornwall were for many years so systematically and exactly reported, and the reports of each were so critically scrutinised by the rival makers, that the data they supply may be relied on without hesitation. It was well known that the best of the engines continuously performed useful work with a consumption of coal at the rate of 2·33 lbs. per delivered horse-power per hour, or, counting coal at 16s. per ton (a fair price on the South Devon), at the cost of ·2d., or one-fifth of a penny per horse-power per hour.
But it was not in its consumption of fuel alone that stationary power was the more economical; the expenditure in wages, oil, and tallow on one of the pumping-engines above referred to, when doing 200 horse-power of useful work, did not exceed 20s. for the twenty-four hours, or one-twentieth of a penny per horse-power per hour, while the cost of repairs was merely nominal.
Thus if fuel, wages, oil, and tallow be brought into one item, it is seen that the cost of one horse-power in stationary engines such as the then existing Cornish engines was only ·25d. per hour, or less than one-fourth of its cost when developed by a locomotive, which has been shown to have been 1·098d. per hour.
[1] See above [2] These quantities are the result of the experiments made in September 1847. They agree with what is now the received opinion of authorities on train resistances, and represent favourably the case for the locomotives at the time of Mr. Brunel’s report in August 1844. At the time when Mr. Brunel wrote his report of August 1844, the weight of a locomotive, as has been said, bore a higher ratio to its power. [3] It must be borne in mind that all the inconveniences attending the use of auxiliary locomotives must be encountered, or else the excessive dead weight of an engine powerful enough to take a train up the steepest gradient in a hilly district must accompany it for the whole length of that part of the line. [4] No dynamometer was used in these experiments, but all other requisite data were recorded with the greatest exactness, and the horse-power employed may be deduced by means of the scale of resistance which the subsequent dynamomotric trials supply. Moreover, the result above arrived at for the consumption of coke is verified by an examination of published indicator diagrams taken off the same engine on another occasion.