262 



METHODS OF CALCULATION 



the reactive flux only occupies a part d of the pitch instead of J, as indi- 

 cated by the dotted intersecting lines in the figure, the reactions will be 

 proportional to the mean ordinates of the areas 12345 and 67,689 

 respectively, limited to the breadth of the flux (which may be different 

 moreover for the transverse flux from what it is for the direct flux. 

 By integrating the area of the sinusoid from H$ on to 54 one finds 



Ordinate of area 12345 = -;; sin ( r)X /o- 



\2 J/ TZ 



Ordinate of area 6 7.680 = v i cos( -. } X /o- 

 L \2 4J] n 



FIG. 17. 



The coefficients which apply to the ampere-turns, resulting from 

 a restriction of the flux, are then respectively for K and K t 



A . /7t8\ A\ /7r<ni 



c=^-sin(--7 and c t = j i-cos (-- , 

 d \ 2 A) dl \ 2 J/J' 



and have the following values for example (not including k) 



f 2 \ 2 



for-r=J; =1.232; ^ = 0.817 from which K=i.2^2[ ) k 

 A \TZ) 



2 

 -) k 



for-^=; =1.299; ^ = 0.75 



=i; =1.414; c ( = 



2 

 -} k 



