96 ALTERNATING CURRENTS 



gives the following values of k for two slots per pole per phase, the 

 slots being th of the pole-pitch apart : 



P ole - arc =0-4 0-5 0-6 07 



pole-pitch 



k = 2-58 2-42 2-3 217 



These values are based on the following assumptions : single 

 air-gap length = ^th of pole-pitch ; radius of curvature of rounded 

 pole-shoe corner = ^o^h of pole-arc ; height of pole-shoe = ^th of 

 pole-arc. 



47. Armature Reaction in Alternators 



When an alternator is loaded, the armature current reacts on the 

 field, distorting and weakening (or, sometimes, strengthening) it. 

 The nature of the armature reaction depends not only on the armature 

 current, but also on its phase relation to the open-circuit or no-load 

 e.m.f. The calculation of the exact effect produced by the armature 

 current in any given case is an extremely laborious matter, and if 

 accuracy is desired, must be carried out separately for each particular 

 type of machine. But the general nature of the effects produced may 

 be easily inferred from the following very simple considerations. 



The currents in the armature windings of a polyphase generator 

 may be assumed to give rise to a rotating wave of magnetic flux 

 ( 20). Since this wave travels around the stator periphery at the 

 same speed as the rotating field-poles,* it will be stationary with 

 respect to the poles. Its position relatively to them will clearly 

 depend on the amount by which the armature current lags or leads, 

 and the nature of the armature reaction will best be understood by 

 considering the three cases of (1) zero phase difference, (2) lag of 

 90, and (3) lead of 90. 



When the current is in phase with the e.m.f. in each phase of the 

 winding, a reference to Figs. 75 or 76 shows that the crest of the 

 rotating wave of flux falls exactly halfway between two pole-pieces, 

 since at the instant when one of the component alternating waves 

 reaches its maximum amplitude, it coincides in position with the 

 resultant rotating wave (see concluding remarks of 20) . The relative 

 position of the field-poles and the rotating wave of magnetic flux is 



* The speed of the rotating wave of magnetic flux is ( 19) ~, \ being the wave- 

 length and T the period. The wave-length, however, corresponds to twice the pole- 

 pitch ; hence is also the speed of the field-poles, each field-pole advancing through a 

 distance equal to twice the pole-pitch during a period. 



