INDUCTION MOTOR 339 



The torque of an induction motor is usually expressed not in 

 foot pounds but in synchronous watts, that is, in terms of the 

 power which would be developed at synchronous speed. 



The torque in synchronous watts is 



N 

 S 



r sync . wat ts = P X % = P r (316) 



and it is equal to the power input to the rotor. 



rr. m n KA TOtor input 



Torque = T = 7.04 - 



sync, speed 



= KEJ 2 cos 6 2 



v r 2 2 -|- s 2 # 2 ' 



'. , r % T 2 , (317) 



/2 ~T~ & X 2 



where K is a constant. 



The following conclusions may be drawn: 



(1) Torque is proportional to the slip near synchronous speed. 



(2) Torque is proportional to E 2 2 and therefore it is approxi- 



mately proportional to the square of the e.m.f. impressed 

 on the stator. 



(3) Torque is maximum when r 2 = sxz. 



(4) Starting torque = KE 2 2 2 * % since s = 1. 



(5) Maximum torque occurs at standstill if r 2 = x 2 . This 



condition can be obtained by inserting resistance in the 

 rotor windings. 



If r 2 ># 2 the starting torque is less than the maximum torque 

 but the starting current is also less than in the case where r 2 = # 2 . 



(6) The current for maximum torque is 



V2 s 2 z 2 2 - \/2 z 2 



and is independent of the rotor resistance. 



214. Rotor Efficiency. Neglecting all losses except the rotor 

 copper loss the rotor efficiency is 



= (1 - s)100% = ^100%, . . (318) 



