272 Introduction to the Study of Science 



Steam engines are well known to be inefficient the most 

 modern type yielding hardly 18 per cent output of work for the 

 100 per cent input of fuel or heat energy. The pulling force, 

 or tractive effort, as it is called by engineers, of an engine is 

 estimated at about one pound to five pounds of weight. Sup- 

 pose an engine, including the tender and its load, weighs one 

 hundred tons ; it has an estimated tractive effort or pull upon 

 the drawbar of twenty tons. It can haul on a level road about 

 four thousand tons. An engine of this size is a pygmy in com- 

 parison with the locomotives of to-day ; but it illustrates the 

 ratio of weight to tractive effort. 



Assume that a trainload of one thousand tons is hauled on 

 a perfectly level track by a pull of five tons. On a road with 

 a rise of fifty-two feet in a mile, or a one per cent grade, the 

 same load will require a tractive effort of fifteen tons. On a 

 two per 'cent grade, the amount of tractive effort needed is 

 about twenty-five tons, or five times that required for a level 

 track. If the grade is two and one half per cent, beyond which 

 engineers prefer not to go, in building railroads, the tractive 

 effort for the same load is about forty tons. This shows why 

 light grades are necessary in order to secure the highest haul- 

 ing efficiency of the road, and to avoid excessive wear and tear 

 on rolling stock and track. The illustration (Fig. 79) shows 

 the combined tractive force of five engines doing on a heavy 

 grade what one engine does easily on a level or even a light 

 grade. 



Grades on transcontinental lines. The data in the accom- 

 panying table show clearly what modern engineering has 

 achieved in building the great transcontinental railroads. 

 Calculate the per cent of grade of each. 



