90 



THE MAGNETIC CIRCUIT 



[ART. 36 



\\ith these assumptions, the permeance of the " simplified " 

 air-gap is 



...... (45) 



where tr, is the average width of the flux, and l s is its average 

 axial length. Or 



eq 



The lateral spread a' of the lines of force at each pole-tip is 

 taken to be approximately equal to a^. 



Ip- 



FIG. 25. Magnetic flux in the simplified air-gap. 



The permeance of the actual air-gap is smaller than that of the 

 simplified gap, so that we have 



....... (46) 



where k a is a coefficient larger than unity, called the air-gap factor. 

 Substituting the value of (P from eq. (46) into (44) gives 



(47) 



so that k a is the factor by which the ampere-turns for the simplified 

 air-gap must be multiplied in order to obtain the ampere-turns 

 required for the actual air-gap. The value of k a usually varies 

 between 1.1 and 1.3, depending on the relative proportions of the 

 teeth, the slots, and the air-gap, and on the shape of the poles. 



The numerical values of fc a are calculated from the results of tests 

 on machines of proportions similar to that being computed. Let 

 the no-load saturation curve of a machine be available from test; 

 this is a curve which gives the relation between the induced voltage 



