112 THE MAGNETIC CIRCUIT [ART. 40 



the opposite side, so that one may be satisfied with a lesser degree 

 of accuracy. The equivalent permeance, reduced to that between 

 the pole-tips, is again equal to one-half the actual permeance, for 

 the same reason as under (b) above. 



The total leakage permeance between a pole and the two planes 

 of symmetry is equal to the sum of the permeances calculated as 

 above. In summing them up it will be seen from Fig. 29 that the 

 permeances (a) and (6) must be taken twice, and also that (c) and 

 (d) must be taken four times. The leakage flux per pole is 

 obtained by multiplying the total leakage permeance by the m.m.f. 

 between the pole-tip and the plane of symmetry. This m.m.f. is 

 equal to that required to establish the useful flux, along the path 

 qrs, through the air-gap and the armature of the machine, and 

 consequently it is known before the pole-piece and the field wind- 

 ing are computed hi detail. Knowing the leakage flux and the 

 useful flux, the leakage factor is figured out according to the defi- 

 nition given above. 



When calculating permeances as indicated above, one is advised 

 to make liberal estimates of the same, for two reasons : In the first 

 place, the true permeance of a path is always the largest possible, so 

 that, whatever assumptions one makes, the calculated permeance 

 comes out smaller than the actual. In the second place, in design- 

 ing a new machine it is better to be on the safe side and rather 

 underestimate than overestimate the excellence of the perform- 

 ance. Some writers give more elaborate rules and formulae for the 

 calculation of the leakage permeance which are useful in the 

 design of machines of special importance. 1 



The leakage factor remains practically constant as long as the 

 flux density in the armature core and teeth is moderate, so that 

 the reluctance of the useful path qrs is nearly constant. This is 

 because the reluctance of the leakage paths is constant, and, if the 

 reluctance of the useful path is also constant, the useful flux and 

 the leakage flux increase in the same proportion when the m.m.f. 

 between the pole-tips is increased. When the armature iron is 

 approaching saturation, the leakage factor increases with the field 



1 For a more detailed treatment of the leakage between poles see the 

 following works: E. Arnold, Die Gleichstrommaschine, Vol. 1 (1906), pp. 

 284-294; Hawkins and Wallis, The Dynamo, Vol. 1 (1909), pp. 469-484; 

 Pichelmayer, Dynamobau (1908), pp. 127-131; Cramp, Continuous-Current 

 Machine Design (1910), pp. 42-47 and 226-230. 



