222 THE DIRECT-CURRENT MOTOR CH. X 



smaller is the acceleration, and the greater the final speed ; 

 hence by increasing we lengthen the period during 



which the motor is accelerating, and during which the 

 maximum current is being drawn from the line. As this 



period is smallest with the smallest value of the 



Mv 



energy expended in covering the given distance will 



decrease with - , so that if -= is greater than the best 

 Mv Mv 



value, the time is longer and the expenditure of energy in 

 accelerating greater, while if -- - is less than the best 



diameter, the time is also longer, but the expenditure of 

 energy in accelerating is less. Hence in order to save 

 energy during the process of acceleration, we should 



increase the ratio - as much as possible, so long as we do 



CL 



not thereby lose too much time in starting. 



We must now consider the effect of changes in the 

 values of V and d upon the total current taken 



from the line. The current required to overcome the re- 

 sistance to motion may be expressed thus : For motor cars, 

 where the resistance may be considered as a constant torque 



of t f inch-pounds on the car axles, we have c,= '71 



showing that c f is independent of d. For locomotives, 

 however, where the resistance to motion may be con- 

 sidered as a constant pull on the draw bar of T pounds, 



Td 



, showing that c f increases with d. 



