94 HIE MAGNETIC CIRCUIT [ART. 37 



where a x is the length of the air-gap at the center of the tooth, and 

 l t ff is the effective axial length of the machine (see below). The 

 value of Jt/ax must be taken from Fig. 26 for the corresponding 

 ratio s/a x . 



The permeance of the pole fringe, hmn in Fig. 24, cannot be cal- 

 culated by the foregoing method, because this permeance depends 

 upon the irregular shape of the pole-tip. The pole-fringe permeance 

 is usually estimated graphically by drawing lines of force, taking 

 Fiir. '_M as a guide 1 ; the permeance of each tube of flux between the 

 pole and the armature is ftA/l, where A is the mean cross-section, 

 and / is the mean length of the tube. The fringe permeance is of 

 the order of magnitude of 10 per cent of the total permeance of 

 the air-gap, so that some error in its estimation does not seriously 

 affect the total required ampere-turns. Careful designers some- 

 times calculate the air-gap permeance for two positions of the 

 pole, differing from each other by one-half of the tooth pitch, and 

 take the average of the two results. 



Carter's curve could be used directly for calculating the pole- 

 fringe permeance, if the pole waist were of the same width as 

 the pole shoe (line mm' in Fig. 24), and if the armature had no 

 slots. In this case the space between the adjacent poles could be 

 considered as a big slot, and the curve in Fig. 26 could be directly 

 applied to it. On account of a smaller width of the pole core and 

 because of the armature slots the mean length of the lines of force 

 in the fringe is increased, so that the actual permeance of the pole- 

 fringe is somewhat smaller than that according to Carter's curve. 

 By practice and experience one can acquire a judgment as to what 

 fraction of Carter's permeance to take in a given case. 



The length l e ff is a sum of the parts such as l if 1%, etc. (Fig. 24), 

 on which the lines of force are parallel, and of small additional 

 lengths which take account of the fringing in the air-ducts and at 

 the pole flanks. These additional lengths are again estimated 

 from Carter's curve (Fig. 26). The fringe Ad in an air-duct of 

 the width d is practically the same as that in a slot of the width 

 s= d. The additional length J/for the pole flanks is found by con- 

 sidering the two fringes as due to a slot of the width /. When the 

 stationary and the revolving parts are of the same axial length so 

 that /= 0, there still remains some fringe permeance between the 



1 See Art. 41 below in regard to the drawing of the lines of force by the 

 judgment of the eye. 



