The life of Isambard Kingdom Brunel, Civil Engineer Part 19

_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 { 1/100 71 50 121 292 263 555 90 40 { 1/75 50 50 100 252 303 555 120 { 1/50 238 50 738 173 382 555 221 { 1/40 117 50 617 113 442 555 391 { 1/363 7 50 57 82 473 555 577 { 0 139 50 189 504 280 784 56 { 1/200 68 50 118 415 369 784 89 { 1/100 357 50 857 325 459 784 141 60 { 1/75 225 50 725 265 519 784 196 { 1/523 7 50 57 160 624 784 390 +------+---------+-------+-------+------+-------+------+------+-----------+

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 cla.s.s 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.[75]

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 45 lbs. of c.o.ke per horse-power per hour may be taken as the average consumption of the engine.[76]

It will be well, however, to allow for the improvement which was at the time antic.i.p.ated in locomotive working, and to a.s.sume an expenditure of 4 lbs. of c.o.ke per indicated horse-power per hour, as representing the case then for the locomotive engine.

c.o.ke may be taken to have at that time cost 21_s._ a ton, or 0094_s._ per lb. Moreover, a careful a.n.a.lysis of the Great Western Railway half-yearly reports, for 1844 and 1845, shows that for every shilling expended in c.o.ke, 144 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 00915_s._ or 1098_d._; that is to say, about 1-1/10_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.