AIR-GAP FLUX DISTRIBUTION 



293 



that would be developed in the windings if all the flux in the air 

 gap were cut by the conductors in the slots. 



The general solution, which includes fractional pitch windings, 

 is illustrated in Fig. 118. The instantaneous value of the aver- 

 age flux density for n slots per pole per phase is 



(a + b + c + ) - (a' + V + c'+ - ) 



B a = 



2n 



The relative positions of the slots and the center of the coil (P) 

 may be marked on a separate strip of paper that can be moved 

 to any desired position under the flux curve; and the'instan- 



Curve of Volts ( e ) Plotted 

 Relatively to Position of 



FIG. 118. Flux curve and resulting e.m.f. wave fractional pitch 

 armature winding. 



taneous values of the voltage can then conveniently be plotted 

 over the point P. For this instantaneous voltage we may write 



Average instantaneous 



e.m.f. per conductor 



= e c = w X 1C' 



= flux cut per centimeter of travel 



X centimeters per second X 10~ 8 

 = (B a la) X v X 1(T 8 



where v 





cm. per second. The instantaneous voltage 



per phase is therefore 



e - e 



as stated in formula (107). 



60X10 8 



