214 THE DIRECT-CURRENT MOTOR CH, X 



but is independent of v, in other words, we can reduce 

 the current required to overcome the frictional resistance 

 by increasing the wheel diameter but not by altering the 



'M.v 

 velocity ratio. Since, however, is given by the final 



Oj 



speed, when d has been fixed we can reduce M by increasing 

 v, i.e. we can lighten the motor by increasing the velocity 

 ratio, although we cannot thereby reduce the running 

 current. We must also note that if we increase d we 

 must at the same time increase M or v to maintain the ratio 



Mv 



P constant. 

 d 



In street railway equipments v is usually taken as large 

 as possible, to reduce the weight of the motor, while the 

 size of the driving wheel is generally limited by structural 

 considerations. 



Example 49a. Take the case of a tramcar. 

 Suppose that the frictional torque per motor is 8,100 inch- 

 pounds at the car axles ; and that we have given ^=500, 

 J?=l-25, M=60, v = 478, d=33" ; maximum current 

 from the line 60 amperes, W=8 tons, series-parallel control. 



Then we get Step I. Frictional current 20 amperes ; 

 accelerating current 6020 = 40 amperes; acceleration 

 3 - 5 2 f.p.s. per second ; time 1*5 seconds. 



STEP II. Accelerating current 30 20 = 10 amperes ; 

 acceleration 0'88 ; time to full speed, assuming acceleration 

 constant, 10 seconds; total time required to start 11 -5 

 seconds. 



Now suppose that we put on 54 instead of 33-inch 

 wheels. To get the same final speed as before, 14'3 f.p.s., or 

 9'75 m.p.h., we must make v = 7'8\. The frictional current 

 is now 1 2 amperes, so that the accelerating current on the 



