2i 4 ALTERNATING CURRENTS 



There is, however, an additional source of loss due to the belt 

 drive which we have so far left out of consideration. This is due 

 to the slipping of the belt on both pulleys. So long as the machines 

 are lightly loaded, the belt slip is inappreciable, and w b represents 

 the only loss taking place outside the machines. But with a heavy 

 load, the rate of heat production at the pulleys due to slipping of 

 the belt over their surfaces may represent an appreciable fraction 

 of the brake-power of the motor. A correction thus becomes neces- 

 sary. If d m = dia. of motor pulley, d g dia. of generator pulley, 

 and t = thickness of belt, all measured in terms of the same unit 

 of length, then the effective diameters of the pulleys are d m + t and 

 d g + t, and if the belt did not slip, the ratio of the speed of the 



generator to that of the motor would be f . .. By reason of 



d g + t 



slipping, however, this is reduced in a certain ratio, say ^ , where 

 b may be termed the belt slip. Thus 



speed of generator pulley _ d m + . _ . 

 speed of motor pulley ~ d g + t^ 



But this ratio may be measured directly. For if s m = slip of motor 

 rotor relatively to its stator field, and s g slip of generator rotor,* 

 we have 



speed of generator rotor _ 1 -f- s g 

 speed of motor rotor ~ 1 s m 



Equating the two expressions for this ratio, we find 

 1 _ i = ^ *" 8 a d m + t 



J. ~~ SM, (t g -j~ t 



Now, if by reason of belt slip the speed of the generator is 



1 I 

 reduced in the ratio ^ , it is obvious that the power transmitted 



to it by the motor is reduced in the same ratio. Thus of the total 

 power w m f developed by the motor a fraction b is lost in producing 

 heat at the pulleys. If i\ m = motor efficiency, approximately calcu- 

 lated as already explained, then in order to balance the loss due 

 to belt slip we have to draw from the mains an amount of power 



7 



-. We have now to recalculate both efficiencies, assuming that 



~ ' O 



*?m 



* Numerical values of the slip being considered (algebraically, the generator slip 

 is negative). 



w tp 4 



Wg + W W b - . 8 m 



