278 PRINCIPLES OF ELECTRICAL DESIGN 



OC, because the magnetizing effect of the (upward) current in 

 the space CA is balanced by that of the (downward) current in 

 the space AC' of equal width, leaving as the effective ampere 

 turns per pole at the point C a band, OC, of conductors, carrying 

 currents in a positive direction, and an equal band, C'O', of con- 

 ductors carrying the same average amount of current in a nega- 

 tive direction. The ampere-conductors in the space of width dd 

 are 



Z'd$ 



cos e x 



pir 



where Z' stands for the total number of inductors on the arma- 

 ture periphery (all phases), and 6 is expressed in radians. Thus 



f* 9 

 Ampere conductors] T Z' I Z' . 



nn \ = I max - I COS 6 dd = - I max SID. 



in space OC J pir I irp 



VQ 



This expression indicates that with an unlimited increase in the 

 number of inductors (and phases) the armature m.m.f. curve of 

 Fig. 108 will be a sine curve when the current variation follows 

 the sine law. 



The maximum value of the armature ampere turns is obtained 



by putting 6 = 7? whence 



(100) 



where I a stands for the virtual or r.m.s. value of the current in 

 the armature conductors. 



This formula may be compared directly with formula 66 (page 

 136), which refers to D.C. machines, by putting it in the form 



Maximum m.m.f. 1 n4 V2Z'I a QA>jrZ'I a 

 (gilberts) per pole I " irp = 1.11 X 2p 



The angle of displacement /3 (Fig. 108) of this curve relatively 

 to the center line of pole depends upon the "internal" power 

 factor, and also upon the displacement of the wave of developed 

 e.m.f., a displacement or distortion which is due to cross-magne^ 

 tization. The angle /3 is not very easily predetermined, but,' 

 once known or assumed, the curve M can be drawn in the correct' 



