CH. VI EFFICIENCY 125 



it follows that the efficiency of conversion can be expressed 

 thus: 



From this we see that for a given resistance and rate of 

 working rj l increases with the tension of the line. We may 



also write : 



7T2 

 K = ^(n l -n l 2 ) ................ (54). 



which shows that for a given efficiency and rate of work- 

 ing the resistance may increase as the square of the 

 tension. 



Example 31. A railway motor has to be designed 

 to drive a car at 20 miles an hour, with a total horizontal 

 effort of 600 pounds. To find the resistance so that the 

 efficiency of conversion shall be 80 per cent on a line of 

 500 volts tension. From Equation 54 we find that R= 1*67 

 ohms. The result should be checked by showing that the 

 current is 60 amperes, the line watts 30,000, and the heat 

 watts 6,000, giving 24,000 for the mechanical watts, and 

 an efficiency of 80 per cent. 



Only a certain proportion of the total mechanical watts 

 is available for useful effort. We shall denote by ij z the 

 ratio of the useful to the total mechanical watts, i.e. the 

 mechanical efficiency. This gives us the ratio of 

 the useful torque to the total torque for any current. 



Let by represent on any convenient scale the curve of 

 total torque for different currents, dg being the maximum 

 torque. Deduct from each ordinate of this curve the 

 torque required to overcome all internal resistance to 

 motion, such as friction, hysteresis, &c., and we shall 



