DESIGN OF ALTERNATORS 



243 



in the preliminary stages of a design, it is usual to assume that 

 the pole shoes are so shaped as to give a sinusoidal distribution 

 of flux over the armature surface. The calculation of a correct- 

 ing factor for distributed windings is then very simple. Thus, 

 if there are two slots per pole per phase in a three-phase machine, 

 there will be six slots per pole pitch, the angular distance between 



180 

 them being -^- = 30 electrical degrees. It is therefore merely 



necessary to add together, vectorially, two quantities having a 

 phase displacement of 30 degrees, each representing the e.m.f. 

 developed in a single conductor. The result, divided by 2, will 

 be the average voltage per conductor of the distributed winding. 

 As an example, with three slots per pole per phase, the graphic 

 construction would be as indicated in Fig. 90 where length 

 AB = length BC = length CD, and what may be called the 



AD 



distribution factor is k = ~o~T5- The value of this distribu- 



FIG. 90. Vector construction to determine distribution factor. 



tion factor is therefore always either equal to, or less than, unity. 

 If Z = the total number of inductors in series per phase, the 

 final formula for the developed voltage is: 



E (per phase) 



X form factor 



(93) 



60 X 10 8 



On the sine wave assumption, the form factor is 1.11, and the 

 formula may, if preferred, be used in the form 



E (per phase) = - ~77vr~~ volts (on sine-wave assumption) (94) 



Values of k can easily be calculated for any arrangement of 

 slots and windings. With a full-pitch three-phase winding, 

 the distribution factor, k, will have the following values : 



Number of slots per pole 

 per phase 



Distribution factor, 



1 1.0 



2 0.966 



3 0.960 



4 0.958 



Infinite. . .0.955 



