96 THE MAGNETIC CIRCUIT [ART. 37 



flank surfaces of the two iron structures. This permeance is, how- 

 ever, very small, and has to be estimated empirically, if at all. 



Strictly speaking, Z c // is different for each tooth, if the air-gap 

 is variable, because the amount of fringing in the air-ducts and at 

 the flanks is different. However, it is hardly worth the effort 

 in ordinary cases to calculate Z e // for each tooth. It is sufficient to 

 take an average Z e // for some intermediate value of the air-gap. 



In some high-speed alternators, and usually in induction 

 motors, air-ducts are provided in both the stationary and the 

 revolving parts, in the same planes. The flux fringe in an air-duct 

 is then of such a shape that the lines of force are parallel to one 

 another in the middle of the air-gap, between the stator and the 

 rotor. Therefore, when using the curve in Fig. 26 for such a case, 

 the cylindrical surface midway between the stator and the rotor 

 must be taken to correspond to that of the solid iron surface 

 assumed in the deduction of the curve. Hence, \a x must be used 

 instead of a x in determining At. 



Having calculated the permeances of the several paths per pole 

 pitch the total permeance of the air-gap is found as their sum, or 



Then, the required number of ampere-turns is determined from 

 eq. (44). The method gives quite correct results, especially with 

 some experience in estimating the permeances of irregular paths. 

 Each designer usually modifies slightly the empirical factors which 

 are indispensable in this method, and devises short cuts good for 

 the particular kind of machine hi which he is interested. 



Instead of calculating the permeance of each tooth separately, 

 some engineers replace the actual variable air-gap by an equiva- 

 lent constant air-gap a e(7 , either by the judgment of the eye, or as 

 in prob. 18 above. The actual peripheral length of the pole arc is 

 increased by from one to one and one-half a eq on each side to take 

 into account the fringing at the pole-tips. This gives the number 

 of teeth under the pole. The permeance of each tooth is calcu- 

 lated from eq. (48) for a x = a eqj and is then multiplied by the num- 

 ber of teeth. With some practice, one can obtain in this manner 

 quite accurate results at a considerable saving in time. 



The method outlined above is not directly applicable to induc- 

 tion machines which have slotted cores on both sides of the air- 



