4IO 



NATURE 



[September 29, 1910 



train-mile were larger, a proportion of the revenue had 

 been used annually for the construction of new works and 

 for the provision of new rolling-stock, instead of raising 

 fresh capital for everything in the nature of an addition 

 to the railway, the companies would to-day have been in 

 a position to regard with equanimity the increasing cost 

 of working. 



It is too" late in the day to recover such a strong financial 

 position, but even now on many lines a larger proportion 

 of the revenue could be sunk in the line with great ultimate 

 advantage to the financial position. 



The Problem of the Locomotive Department. 



During the last twenty years the demand on the loco- 

 motive has steadily increased. The demand has been met, 

 though with increasing difliculty, owing to the constructive 

 limitations imposed by the gauge. The transference of a 

 train from one place to another requires that work should 

 be done continuously by the locomotive against the tractive 

 resistance. The size of the locomotive is determined by 

 the rate at which this work is to be done. If T represents 

 the tractive resistance at any instant, and V the speed of 

 the train, then the rate at which work is done is expressed 

 by the product TV. The pull exerted by the locomotive 

 must never be less than the resistance of the whole train 

 considered as a dead load on the worst gradient and curve 

 combination on the road, and it can never be greater than 

 about one-quarter of the total weight on the coupled wheels 

 of the engine. 



.'\gain, the tractive pull of the engine may be analysed 

 into two parts — one the pull exerted to increase the speed 

 of the train, the other the pull required to maintain the 

 speed when once it has been reached. For an express 

 train the number of seconds required to attain the journey 

 speed is so small a fraction of the total time interval 

 between the stops that the question of acceleration is not 

 one of much importance. But for a local service where 

 stops are frequent the time required to attain the journey 

 speed from rest is so large a fraction of the time between 

 'itops that this consideration dominates the design of the 

 vjcomotive, and, in fact, makes it desirable to substitute 

 (he electric motor for the locomotive in many cases. 



An accurate estimate of the rate at which work must 

 be done to run a stated service can only be made if there 

 are given the weight of the vehicles in the train, the 

 weight of the engine, the kind of stock composing the 

 train, the speed and acceleration required at each point 

 of the journey and a section of the road; and, in addition 

 to this, allowance must be made for weather conditions. 



A general idea of the problem can, however, be obtained 

 by omitting the consideration of acceleration, gradients, 

 and the unknown factor of weather conditions, considering 

 only the rate at which work must be done to draw a 

 given load at a given speed on the level. Even thus 

 simplified the problem can be solved only approximately, 

 because, although the tractive resistance of a train as a 

 whole is a function of the speed, the tractive resistance 

 per ton of load of the vehicles and per ton of load of the 

 engine differ both in absolute value and in their rates of 

 change for a stated speed, and, further, the ratio between 

 the weight of the vehicles and the weight of the engine is 

 a very variable quantity. 



For our purpose, however, it will be sufificiently accurate 

 to assume that the resistance of the whole train, expressed 

 in pounds per ton, is given by the formula 



T = 5J- 



256 



It follows that the horse-power which must be developed 

 at the driving-wheels to maintain a speed of V miles per 

 hour on the level with a train weighing W tons is 



f V V^ 1 

 I 70 96,000 I 



Fig. 5 shows curves of horse-power plotted from this 

 equation for various weights of train. From this diagram 

 a glimpse of the problem confronting locomotive engineers 

 at the present day can readily be obtained. 



To illustrate the point, consider the case of the Scotch 



NO. 2135, VOL. 84] 



express on the West Coast route.' This is an historic 

 service, and goes away back to 1844, in which year the 

 first train left Huston for Carlisle, travelling by way of 

 Rugby, Leicester, York, and Newcastle, and occupying 

 15.^ hours. It was not until 1847, however, that there 

 was a through service to Edinburgh via Berwick. 



In September, 1848, the West Coast service for Edin- 

 burgh was established by way of Birmingham and Carlisle, 

 the timing being 8 hours 55 minutes to Carlisle, and 

 12 hours to Edinburgh. 



In September, 1863, the starting time from Euston was 

 fixed at 10 a.m., and in 1875 the train ran via the Trent 

 Valley between Rugby and Stafford, thus cutting out 

 Birmingham and shortening the journey to Carlisle from 

 309 miles to 299 miles, the timing being 7 hours 42 minutes 

 to Carlisle, and 10 hours and 25 minutes to Edinburgh. 

 The speed has gradually been increased, and in 1905 the 

 timing was 5 hours 54 minutes to Carlisle, and 8J hours 

 to Edinburgh. Now the timing is 5 hours 48 minutes to 

 Carlisle, but is still 8J hours to Edinburgh. 



Three specific examples are plotted on the diagram, 

 showing the power requirements in 1864, 1885, and 1903 

 for this train. Typical trains in 1864, 1885, and 1903 

 weighed, including engine and tender, 100 tons, 250 tons, 

 and 450 tons respectively. The average speeds were thirty- 



MILES PER HOUR. 



eight, forty-five, and fifty-two miles per hour respectively. 

 .'V glance at the diagram will show that the power required 

 to work this train was about 100 horse-power in 1S64, 

 400 horse-power in 1885, and 1000 horse-power in 1903. 



It must not be supposed that the increase in the weight 

 of the train means a proportionate increase in the paying 

 load. Far from it. On a particular day in 1903, when 

 the total weight of the Scotch express was 450 tons 

 approximately, the weight of the vehicles was about 346 

 tons. There were two dining-cars on the train, and the 

 seating accommodation, exclusive of the seats in the 

 dining-cars, was for 247 passengers, giving an pverage of 

 1-4 tons of dead load to be hauled by the engine per 

 passenger, assuming the train to be full. In the days 

 before corridor stock and dining-cars were invented the 

 dead load to be hauled was about a quarter of a ton per 

 passenger for a full train. 



In a particular boat special, consisting of two first-class 

 saloons, one second- and third-class vehicles, one first- 

 class dining-car, one second and third-class dining-car, 

 one kitchen-car, and two brake-vans, seating accommoda- 

 tion was provided, exclusive of the dining-cars, for 104 

 passengers, and the dead load to be hauled averaged 2'72 



1 I am indebted 

 Express Service. 



Mr 



Bowen Cooke for particulars of the Scotch 



