September 29, 1910] 



NATURE 



411 



tons per passenger. Notwithstanding this increase in the 

 dead load of luxurious accommodation, the fares are now 

 less than in former days on corresponding services. 

 Similar developments have taken place in almost every 

 important service, and new express services are all 

 characterised by heavy trains and high speeds. 



Characteristic Energy-curves of Steam Locomotives. 



This steadily increasing demand for power necessarily 

 directs attention to the problem. What is the maximum 

 power which can be obtained from a locomotive within 

 the limits of the construction-gauge obtaining on British 

 railways? The answer to this can be found without much 

 ambiguity from a diagram which I have devised, consist- 

 ing of a set of typical characteristic energy-curves to 

 represent the transference and transformation of energy 

 in a steam locomotive, an example of which is given in 

 Fig. 6. While examining the records of a large number 

 ol locomotive trials, I discovered that if the indicated 

 horse-power be plotted against the rate at which heat 

 energy is transferred across the boiler-heating surface the 

 points fall within a straight-line region, providing that 

 the regulator is always full open and that the power is 



i-= ^Typical Characteristic Energy Curves — 

 ,,.. or Steam Locomotives.- ■ i 



100000 2DP0OO »0000 40000<t 500000 600000 70OO0O 

 8TU TRANSFERRCO ACROSS M.& PER MIN. 



regulated by means of the reversing lever — that is to say, 

 by varying the cut-off in the cylinders. It is assumed at 

 the same time, of course, that the boiler-pressure is main- 

 tained constant. I have recently drawn a series of 

 characteristic energy-curves for particular engines, and 

 these are published in Engineering, August 19 and 26, 

 19 10. A typical set is shown in Fig. 6. 



The horizontal scale represents the number of British 

 thermal units transferred across the boiler-heating surface 

 per minute. This quantity is used as an independent 

 variable. Plotted vertically are corresponding horse- 

 powers, each experiment being shown by a black dot on 

 the diagram. The small figures against the dots denote 

 the speed in revolutions of the crank-axle per minute. 

 Experiments at the same speed are linked by a faint chain- 

 dotted line. A glance at the diagram will show at once 

 how nearly all the experiments fall on a straight line, 

 notwithstanding the wide range of speed and power. 



The ordinates of the dotted curve just below the I.H.P. 

 curve represent the heat energy in the coal shovelled per 

 minute into the fire-box — that is, the rate at which energy 

 is supplied to the locomotive. The thick line immediately 

 beneath it represents the energy produced by combustion. 



NO. 2135, VOL. 84] 



The vertical distance between these two curves represents 

 energy unproduced, but energy which might have been 

 produced under more favourable conditions of combustion. 

 Some of the unproduced energy passes out of the chimney- 

 top in carbon monoxide gas, but the greater proportion 

 is found in the partially consumed particles of fuel thrown 

 out at the chimney-top in consequence of the fierce draught 

 which must be used to burn the coal in suflicient quantity 

 to produce energy at the rate required. The rate of com- 

 bustion is measured by the number of pounds of fuel 

 burnt per square foot of grate per hour. In l^nd practice, 

 with natural draft, 20 lb. of coal per square foot of grate 

 per hour is a maximum rate. In a locomotive the rate 

 sometimes reaches 150 lb. per square foot per hour. In 

 the diagram shown the maximum rate is about 120 lb. 

 per square foot, and the dotted curve begins to turn 

 upwards at about 70 lb. per square foot per hour. The 

 vertical distance between the curves shows what has to be 

 paid for high rates of combustion. 



I found that in almost every case the curve representing 

 the energy actually produced by combustion differed very 

 little from a straight line, passing through the origin, 

 showing that at all rates of working the efficiency of 

 transmission is approximately constant. That is to say, 

 the proportion of the heat energy actually produced by 

 combustion in the fire-bo.x which passes across the boiler- 

 heating surface per minute is nearly constant, and is 

 therefore independent of the rate of working. 



The lowest curve on the diagram represents the rate 

 at which heat energy is transformed into mechanical 

 energy in the cylinders of the locomotive. It seems a 

 small rate in proportion to the rate at which heat energy 

 is supplied to the fire-box, but it is not really so bad as 

 it looks, because the engine actually transformed 60 per 

 cent, of the energy which would have been transformed 

 by a perfect engine working on the Rankine cycle between 

 the same limits of pressure. The engine efficiency is repre- 

 sented in a familiar way by a curve labelled " B.T.H. per 

 I.H.P. minute." It will be seen that the change of 

 efficiency is small, notwithstanding large changes in the 

 indicated horse-power. 



The diagram indicates that the indicated horse-power is 

 practically proportional to the rate at which heat is trans- 

 ferred across the boiler-heating surface, and as this is 

 again proportional to the extent of the heating surface, the 

 limit of economical power is reached when the dimensions 

 of the boiler have reached the limits of the construction- 

 gauge, the boiler being provided with a fire-grate of such 

 size that, at ma.ximum rate of working, the rate of com- 

 bustion falls between 70 and 100 lb. of coal per square 

 foot of grate per hour. A boiler of large heating surface 

 may be made with a small grate, necessitating a high rate 

 of combustion to obtain the required rate of heat-produc- 

 tion. Then, although a large power may be obtained, it 

 will not be obtained economically. 



Returning now to the consideration of the type of loco- 

 motive required for a local service with frequent stops, 

 the problem is to provide an engine which will get into 

 its stride in the least time consistent with the comfort of 

 the passengers. The average speed of a locomotive on 

 local service is low. The greater part of the time is 

 occupied in reaching the journey speed, and the brake 

 must then often be applied for a stop a few moments after 

 the speed has been attained. In some cases the stations 

 are so Close together that there is no period between 

 acceleration and retardation. Without going into the 

 details of the calculation, I may say that to start from 

 rest a train weighing, including the engine, 300 tons, and 

 to attain a speed of thirty miles per hour in thirty seconds 

 requires about 1350 indicated horse-power. During the 

 period of acceleration the engine must exert an average 

 tractive pull of nearly fifteen tons. 



Mr. James Holden, until recently locomotive engineer 

 of the Great Eastern Railway, built an engine to produce 

 an acceleration of thirty miles per hour in thirty seconds 

 with a gross load of 300 tons. The engine weighed 78 

 tons, and was supported on ten coupled wheels, each 

 4 feet 6 inches diameter. There were three high-pressure 

 cylinders, each i8i inches diameter and 24 inches stroke. 

 A boiler was provided with 3000 square feet of heating 

 surface and a grate of 42 square feet area. Boiler 



